Which of the following is a factor of (x+ y)3 – (x3 + y3) ? -Maths 9th

Which of the following is a factor of (x+ y)3 – (x3 + y3) ? -Maths 9th
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Which of the following is a factor of (x+ y)3 – (x3 + y3) ? -Maths 9th

Description : Which of the following is a factor of (x+ y)3 – (x3 + y3) ? -Maths 9th

Last Answer : This answer was deleted by our moderators...

Find the value of x3 +y3 -12xy + 64,when x+y = -4. -Maths 9th

Description : Find the value of x3 +y3 -12xy + 64,when x+y = -4. -Maths 9th

Last Answer : Find the value of

Find the value of x3 +y3 -12xy + 64,when x+y = -4. -Maths 9th

Description : Find the value of x3 +y3 -12xy + 64,when x+y = -4. -Maths 9th

Last Answer : Find the value of

Find the value of x3 + y3 + z3 – 3xyz if x2 + y2 + z2 = 83 and x + y + z = 15 -Maths 9th

Description : Find the value of x3 + y3 + z3 – 3xyz if x2 + y2 + z2 = 83 and x + y + z = 15 -Maths 9th

Last Answer : Consider the equation x + y + z = 15 From algebraic identities, we know that (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) So, (x + y + z)2 = x2 + y2 + z2 + 2(xy + yz + xz) From the question, x2 + y2 + z2 ... y3 + z3 - 3xyz = 15(83 - 71) => x3 + y3 + z3 - 3xyz = 15 12 Or, x3 + y3 + z3 - 3xyz = 180

Find the value of x3+y3+12xy-64 when x=4 -Maths 9th

Description : Find the value of x3+y3+12xy-64 when x=4 -Maths 9th

Last Answer : On the value of x we put the value 4 When it is in power 64+y3+12x4y-64 64+y3+48y-64 64-64+y3+48y 0+y(y2+48) Y(y2+48)

Find the remainder when y3 + y2 - 2y + 5 is divided by y - 5. -Maths 9th

Description : Find the remainder when y3 + y2 - 2y + 5 is divided by y - 5. -Maths 9th

Last Answer : Remainder = 145 Again, we should evaluate p(5) Let p(y) = y3 + y2 - 2y + 5 ∴ p(5) = 53 + 52 - 2 x 5 + 5 = 125 + 25 - 10 + 5 = 145 Thus , we find that p(5) is the remainder when p(y) is divided by y - 5 .

Find the remainder when y3 + y2 - 2y + 5 is divided by y - 5. -Maths 9th

Description : Find the remainder when y3 + y2 - 2y + 5 is divided by y - 5. -Maths 9th

Last Answer : Remainder = 145 Again, we should evaluate p(5) Let p(y) = y3 + y2 - 2y + 5 ∴ p(5) = 53 + 52 - 2 x 5 + 5 = 125 + 25 - 10 + 5 = 145 Thus , we find that p(5) is the remainder when p(y) is divided by y - 5 .

Determine which of the following polynomials has (x + 1) a factor: (i) x3+x2+x+1 -Maths 9th

Description : Determine which of the following polynomials has (x + 1) a factor: (i) x3+x2+x+1 -Maths 9th

Last Answer : Solution: Let p(x) = x3+x2+x+1 The zero of x+1 is -1. [x+1 = 0 means x = -1] p(−1) = (−1)3+(−1)2+(−1)+1 = −1+1−1+1 = 0 ∴By factor theorem, x+1 is a factor of x3+x2+x+1

Show that, x + 3 is a factor of 69 + 11c – x2 + x3 -Maths 9th

Description : Show that, x + 3 is a factor of 69 + 11c – x2 + x3 -Maths 9th

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Show that, x + 3 is a factor of 69 + 11c – x2 + x3 -Maths 9th

Description : Show that, x + 3 is a factor of 69 + 11c – x2 + x3 -Maths 9th

Last Answer : This answer was deleted by our moderators...

If x-2 is a factor of x3-3x+5a then find the value of a -Maths 9th

Description : If x-2 is a factor of x3-3x+5a then find the value of a -Maths 9th

Last Answer : -2/5 is value of a

If x-2 is a factor of x3-3x+5a then find the value of a -Maths 9th

Description : If x-2 is a factor of x3-3x+5a then find the value of a -Maths 9th

Last Answer : This answer was deleted by our moderators...

Using factor theorem, factorise the polynomial x3 + x2 - 4x - 4. -Maths 9th

Description : Using factor theorem, factorise the polynomial x3 + x2 - 4x - 4. -Maths 9th

Last Answer : Solution :-

p(x)=x3+3x2+3x+1, g(x) = x+2 -Maths 9th

Description : p(x)=x3+3x2+3x+1, g(x) = x+2 -Maths 9th

Last Answer : p(x) = x3+3x2+3x+1, g(x) = x+2 g(x) = 0 ⇒ x+2 = 0 ⇒ x = −2 ∴ Zero of g(x) is -2. Now, p(−2) = (−2)3+3(−2)2+3(−2)+1 = −8+12−6+1 = −1 ≠ 0 ∴By factor theorem, g(x) is not a factor of p(x

For what value of m is x3 -2mx2 +16 divisible by x + 2 ? -Maths 9th

Description : For what value of m is x3 -2mx2 +16 divisible by x + 2 ? -Maths 9th

Last Answer : Let p(x) = x3 -2mx2 +16 Since, p(x) is divisible by (x+2), then remainder = 0 P(-2) = 0 ⇒ (-2)3 -2m(-2)2 + 16=0 ⇒ -8-8m+16=0 ⇒ 8 = 8 m m = 1 Hence, the value of m is 1 .

For what value of m is x3 -2mx2 +16 divisible by x + 2 ? -Maths 9th

Description : For what value of m is x3 -2mx2 +16 divisible by x + 2 ? -Maths 9th

Last Answer : Let p(x) = x3 -2mx2 +16 Since, p(x) is divisible by (x+2), then remainder = 0 P(-2) = 0 ⇒ (-2)3 -2m(-2)2 + 16=0 ⇒ -8-8m+16=0 ⇒ 8 = 8 m m = 1 Hence, the value of m is 1 .

p(x)=x3-2x2-4x-1, g(x)=x- -Maths 9th

Description : p(x)=x3-2x2-4x-1, g(x)=x- -Maths 9th

Last Answer : NEED ANSWER

p(x)=x3-2x2-4x-1, g(x)=x- -Maths 9th

Description : p(x)=x3-2x2-4x-1, g(x)=x- -Maths 9th

Last Answer : This answer was deleted by our moderators...

Find the value of x3-8y3-36xy-216 when x = 2y+6. -Maths 9th

Description : Find the value of x3-8y3-36xy-216 when x = 2y+6. -Maths 9th

Last Answer : Solution :-

factorize x3-2x2-x+2 -Maths 9th

Description : factorize x3-2x2-x+2 -Maths 9th

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Factorise: x3 +13x2 + 32x + 20. -Maths 9th

Description : Factorise: x3 +13x2 + 32x + 20. -Maths 9th

Last Answer : Solution :-

If x2 + 1/x2 = 34, find x3 + 1/x3 - 9. -Maths 9th

Description : If x2 + 1/x2 = 34, find x3 + 1/x3 - 9. -Maths 9th

Last Answer : Solution :-

Using factor theorem,show that (x-y) is a factor of x(y(square) - z(square)) + y(z(square) - x(square)) + z(x(square) - y(square) ) -Maths 9th

Description : Using factor theorem,show that (x-y) is a factor of x(y(square) - z(square)) + y(z(square) - x(square)) + z(x(square) - y(square) ) -Maths 9th

Last Answer : Solution :-

The standard equation of a cubic parabolic transition curve provided on roads, is (A) y = x3 /6 RL (B) y = x/6 RL (C) y = l²/6 RL (D) y = l3 /6 RL

Description : The standard equation of a cubic parabolic transition curve provided on roads, is (A) y = x3 /6 RL (B) y = x/6 RL (C) y = l²/6 RL (D) y = l3 /6 RL

Last Answer : Answer: Option A

The standard equation of a cubical spiral transition curve provided on roads, is (A) y = l²/6RL (B) y = x3 /6RL (C) y = x2 /6RL (D) y = x/6RL

Description : The standard equation of a cubical spiral transition curve provided on roads, is (A) y = l²/6RL (B) y = x3 /6RL (C) y = x2 /6RL (D) y = x/6RL

Last Answer : Answer: Option B

Find the value of k,if y+3 is a factor of 3y(to the power square) + ky + 6. -Maths 9th

Description : Find the value of k,if y+3 is a factor of 3y(to the power square) + ky + 6. -Maths 9th

Last Answer : Solution :-

Check whether the following are quadratic equations: (i) (x+ 1)2=2(x-3) (ii) x – 2x = (- 2) (3-x) (iii) (x – 2) (x + 1) = (x – 1) (x + 3) (iv) (x – 3) (2x + 1) = x (x + 5) (v) (2x – 1) (x – 3) = (x + 5) (x – 1) (vi) x2 + 3x + 1 = (x – 2)2 (vii) (x + 2)3 = 2x(x2 – 1) (viii) x3 -4x2 -x + 1 = (x-2)3 -Maths 10th

Description : Check whether the following are quadratic equations: (i) (x+ 1)2=2(x-3) (ii) x - 2x = (- 2) (3-x) (iii) (x - 2) (x + 1) = (x - 1) (x + 3) (iv) (x - 3) (2x + 1) = x (x + 5) (v) (2x - 1) (x - 3) = (x ... vi) x2 + 3x + 1 = (x - 2)2 (vii) (x + 2)3 = 2x(x2 - 1) (viii) x3 -4x2 -x + 1 = (x-2)3 -Maths 10th

Last Answer : this is the correct answer!

Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases: (i) p(x) = 2x3+x2–2x–1, g(x) = x+1 -Maths 9th

Description : Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases: (i) p(x) = 2x3+x2–2x–1, g(x) = x+1 -Maths 9th

Last Answer : Solution: p(x) = 2x3+x2–2x–1, g(x) = x+1 g(x) = 0 ⇒ x+1 = 0 ⇒ x = −1 ∴Zero of g(x) is -1. Now, p(−1) = 2(−1)3+(−1)2–2(−1)–1 = −2+1+2−1 = 0 ∴By factor theorem, g(x) is a factor of p(x

Show that x + a is a factor of xn + an for any odd +ve integer n. -Maths 9th

Description : Show that x + a is a factor of xn + an for any odd +ve integer n. -Maths 9th

Last Answer : Let f(x) = xn + an x + a will be the factor of xn + an if f(-a) = 0 Now f(-a) = (-a)n + an = 0 (since n is a odd +ve integer) Thus (x +a) is a factor of xn + an .

If x + 1 is a factor of the polynomial 2x2 + kx, then the value of k is -Maths 9th

Description : If x + 1 is a factor of the polynomial 2x2 + kx, then the value of k is -Maths 9th

Last Answer : (c) Let p(x) = 2x2 + kx Since, (x + 1) is a factor of p(x), then p(-1)=0 2(-1)2 + k(-1) = 0 ⇒ 2-k = 0 ⇒ k= 2 Hence, the value of k is 2.

x + 1 is a factor of the polynomial -Maths 9th

Description : x + 1 is a factor of the polynomial -Maths 9th

Last Answer : (b) Let assume (x + 1) is a factor of x3 + x2 + x+1. So, x = -1 is zero of x3 + x2 + x+1 (-1)3 + (-1)2 + (-1) + 1 = 0 ⇒ -1+1-1 + 1 = 0 ⇒ 0 = 0 Hence, our assumption is true.

Determine which of the following polynomial has x – 2 a factor -Maths 9th

Description : Determine which of the following polynomial has x – 2 a factor -Maths 9th

Last Answer : first option is the correct answer for the given question solution is as follows:- let x-2=0 then, x=2 put x in (i) 3(2)(2)+6(2)-24=0 12+12-24=0 {use BODMAS rule for solution}... 24-24=0 0=0 this verifies our answer

If x + 2a is a factor of a5 -4a2x3 +2x + 2a +3, then find the value of a. -Maths 9th

Description : If x + 2a is a factor of a5 -4a2x3 +2x + 2a +3, then find the value of a. -Maths 9th

Last Answer : Let p(x) = a5 -4a2x3 +2x + 2a +3 Since, x + 2a is a factor of p(x), then put p(-2a) = 0 (-2a)5 – 4a2 (-2a)3 + 2(-2a) + 2a + 3 = 0 ⇒ -32a5 + 32a5 -4a + 2a+ 3 = 0 ⇒ -2a + 3 = 0 2a =3 a = 3/2. Hence, the value of a is 3/2.

If x +1 is a factor of ax3 +x2 -2x + 4a - 9, then find the value of a. -Maths 9th

Description : If x +1 is a factor of ax3 +x2 -2x + 4a - 9, then find the value of a. -Maths 9th

Last Answer : The value of a

Show that x + a is a factor of xn + an for any odd +ve integer n. -Maths 9th

Description : Show that x + a is a factor of xn + an for any odd +ve integer n. -Maths 9th

Last Answer : Let f(x) = xn + an x + a will be the factor of xn + an if f(-a) = 0 Now f(-a) = (-a)n + an = 0 (since n is a odd +ve integer) Thus (x +a) is a factor of xn + an .

If x + 1 is a factor of the polynomial 2x2 + kx, then the value of k is -Maths 9th

Description : If x + 1 is a factor of the polynomial 2x2 + kx, then the value of k is -Maths 9th

Last Answer : (c) Let p(x) = 2x2 + kx Since, (x + 1) is a factor of p(x), then p(-1)=0 2(-1)2 + k(-1) = 0 ⇒ 2-k = 0 ⇒ k= 2 Hence, the value of k is 2.

x + 1 is a factor of the polynomial -Maths 9th

Description : x + 1 is a factor of the polynomial -Maths 9th

Last Answer : (b) Let assume (x + 1) is a factor of x3 + x2 + x+1. So, x = -1 is zero of x3 + x2 + x+1 (-1)3 + (-1)2 + (-1) + 1 = 0 ⇒ -1+1-1 + 1 = 0 ⇒ 0 = 0 Hence, our assumption is true.

Determine which of the following polynomial has x – 2 a factor -Maths 9th

Description : Determine which of the following polynomial has x – 2 a factor -Maths 9th

Last Answer : first option is the correct answer for the given question solution is as follows:- let x-2=0 then, x=2 put x in (i) 3(2)(2)+6(2)-24=0 12+12-24=0 {use BODMAS rule for solution}... 24-24=0 0=0 this verifies our answer

If x + 2a is a factor of a5 -4a2x3 +2x + 2a +3, then find the value of a. -Maths 9th

Description : If x + 2a is a factor of a5 -4a2x3 +2x + 2a +3, then find the value of a. -Maths 9th

Last Answer : Let p(x) = a5 -4a2x3 +2x + 2a +3 Since, x + 2a is a factor of p(x), then put p(-2a) = 0 (-2a)5 – 4a2 (-2a)3 + 2(-2a) + 2a + 3 = 0 ⇒ -32a5 + 32a5 -4a + 2a+ 3 = 0 ⇒ -2a + 3 = 0 2a =3 a = 3/2. Hence, the value of a is 3/2.

If x +1 is a factor of ax3 +x2 -2x + 4a - 9, then find the value of a. -Maths 9th

Description : If x +1 is a factor of ax3 +x2 -2x + 4a - 9, then find the value of a. -Maths 9th

Last Answer : The value of a

Show that x+a is a factor of x^n+a^n for any odd positive n -Maths 9th

Description : Show that x+a is a factor of x^n+a^n for any odd positive n -Maths 9th

Last Answer : Let f(x)=xn+an. In order to prove that x+a is a factor of f(x) for any odd positive integer n, it is sufficient to show that f(−a)=0. f(−a)=(−a)n+an=(−1)nan+an f(−a)=(−1+1)an [ n is odd positive integer ] f(−a)=0×an=0 Hence, x+a is a factor of xn+an, when n is an odd positive integer.

Show that x+a is a factor of x^n+a^n for any odd positive n -Maths 9th

Description : Show that x+a is a factor of x^n+a^n for any odd positive n -Maths 9th

Last Answer : This answer was deleted by our moderators...

If x+1 is a factor of the polynomial 3x(square) - kx,then find the value of k. -Maths 9th

Description : If x+1 is a factor of the polynomial 3x(square) - kx,then find the value of k. -Maths 9th

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Find the value of a, if x-a is a factor of x(cube) - ax(square) + a-1. -Maths 9th

Description : Find the value of a, if x-a is a factor of x(cube) - ax(square) + a-1. -Maths 9th

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If x(square) - 1 is a factor of ax(cube) + bx(square) + cx + d,show that a+c=0. -Maths 9th

Description : If x(square) - 1 is a factor of ax(cube) + bx(square) + cx + d,show that a+c=0. -Maths 9th

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If (x+1) is a factor of ax(cube) + x(square) - 2x + 4a - 9,find the value of a. -Maths 9th

Description : If (x+1) is a factor of ax(cube) + x(square) - 2x + 4a - 9,find the value of a. -Maths 9th

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For what value of k,(x+1) is a factor of p(x) - kx(square) - x - 4 ? -Maths 9th

Description : For what value of k,(x+1) is a factor of p(x) - kx(square) - x - 4 ? -Maths 9th

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Find the value of k if (x-2)is a factor of polynomial p(x) = 2x(cube) - 6x(square) + 5x + k. -Maths 9th

Description : Find the value of k if (x-2)is a factor of polynomial p(x) = 2x(cube) - 6x(square) + 5x + k. -Maths 9th

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If (x^2 – 1) is a factor of ax^4 + bx^3 + cx^2 + dx + e, then : -Maths 9th

Description : If (x^2 – 1) is a factor of ax^4 + bx^3 + cx^2 + dx + e, then : -Maths 9th

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If (x + k) is a common factor of x^2 + px + q and x^2 + lx + m, then the value of k is -Maths 9th

Description : If (x + k) is a common factor of x^2 + px + q and x^2 + lx + m, then the value of k is -Maths 9th

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