Factorise: 2x(square) - 7x -15 by spliting the middle term. -Maths 9th

Factorise: 2x(square) - 7x -15 by spliting the middle term. -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

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Expand using suitable identity (-2x + 5y - 3z) to the whole square. -Maths 9th

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What must be added to 2x(square) - 5x + 6 to get x(cube) - 3x(square) + 3x - 5? -Maths 9th

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Check whether polynomial p(x) = 2x(cube) - 9x(square) + x + 12 is a multiple of 2x-3 or not. -Maths 9th

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3. Check whether 7+3x is a factor of 3x3+7x. -Maths 9th

Description : 3. Check whether 7+3x is a factor of 3x3+7x. -Maths 9th

Last Answer : Solution: 7+3x = 0 ⇒ 3x = −7 ⇒ x = -7/3 ∴Remainder: 3(-7/3)3+7(-7/3) = -(343/9)+(-49/3) = (-343-(49)3)/9 = (-343-147)/9 = -490/9 ≠ 0 ∴7+3x is not a factor of 3x3+7x

One of the zeroes of the polynomial 2x2 + 7x – 4 is -Maths 9th

Description : One of the zeroes of the polynomial 2x2 + 7x – 4 is -Maths 9th

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Last Answer : Let p(x) =3x3 – 4x2 + 7x – 5 At x= 3, p(3) = 3(3)3 – 4(3)2 + 7(3) – 5 = 3×27-4×9 + 21-5 = 81-36+21-5 P( 3) =61 At x = -3, p(-3)= 3(-3)3 – 4(-3)2 + 7(-3)- 5 = 3(-27)-4×9-21-5 = -81-36-21-5 = -143 p(-3) = -143 Hence, the value of the given polynomial at x = 3 and x = -3 are 61 and -143, respectively.

One of the zeroes of the polynomial 2x2 + 7x – 4 is -Maths 9th

Description : One of the zeroes of the polynomial 2x2 + 7x – 4 is -Maths 9th

Last Answer : (b) Let p (x) = 2x2 + 7x-4 = 2x2 + 8x-x-4 [by splitting middle term] = 2x(x+ 4)-1(x+ 4) = (2x-1)(x+ 4) For zeroes of p(x), put p(x) = 0 ⇒ (2x -1) (x + 4) = 0 ⇒ 2x-1 = 0 and x+4 = 0 ⇒ x = 1/2 and x = -4 Hence, one of the zeroes of the polynomial p(x) is 1/2.

Find the value of the polynomial 3x3 – 4x2 + 7x – 5, when x = 3 and also when x = -3. -Maths 9th

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Last Answer : Let p(x) =3x3 – 4x2 + 7x – 5 At x= 3, p(3) = 3(3)3 – 4(3)2 + 7(3) – 5 = 3×27-4×9 + 21-5 = 81-36+21-5 P( 3) =61 At x = -3, p(-3)= 3(-3)3 – 4(-3)2 + 7(-3)- 5 = 3(-27)-4×9-21-5 = -81-36-21-5 = -143 p(-3) = -143 Hence, the value of the given polynomial at x = 3 and x = -3 are 61 and -143, respectively.

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Last Answer : Let α, β be the roots of the equation 7x2 + 12x + 18 = 0. ∴ Required ratio = α2 + β2 : αβ = ​​−10849187 = −67 = – 6 : 7.

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If (x + 1) is a factor of x^4 + 9x^3 + 7x^2 + 9ax + 5a^2, then : -Maths 9th

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The acute angle which the perpendicular from the origin on the line 7x –3y = 4 makes with the x-axis is: -Maths 9th

Description : The acute angle which the perpendicular from the origin on the line 7x –3y = 4 makes with the x-axis is: -Maths 9th

Last Answer : (c) negativeAs the line from the origin is perpendicular to the line 7x - 3y = 4, so its slope = \(rac{-1}{ ext{slope of }\,7x-3y=4}\)Slope of 7x - 3y - 4 = \(rac{7}{3}\)∴ Slope of line from origin = \(rac{-1} ... of x-axis⇒ θ = tan-1 \(\big(rac{-3}{7}\big)\) = - tan-1 \(\big(rac{3}{7}\big)\)

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Factorise each of the following expressions: -Maths 9th

Description : Factorise each of the following expressions: -Maths 9th

Last Answer : (i) 48x3 - 36x2 = 12.4 x2 x - 12.3x2 = 12x2 (4x - 3) (ii) 5x2 - 15xy = 5x (x-3y) (iii) 15x3y2z - 25xy2z3 = 5xy2z(3x2 - 5z2)

Factorise this question -Maths 9th

Description : Factorise this question -Maths 9th

Last Answer : (i) The greatest monomial that is a common factor of the three terms is 6xy. ∴ 30x3y + 24x2y2 - 6xy = 6xy (5x2 + 4xy - 1) (ii) Here the polynomial (a-b) is a common factor. ∴ 5x(a-b) + 6y(a-b) = (a-b) (5x + 6y)

Factorise this question -Maths 9th

Description : Factorise this question -Maths 9th

Last Answer : (i) 7a3 + 7a - 2a2 - 2 = 7a(a2 + 1) - 2 (a2 + 1) = (a2 + 1) (7a - 2) (ii) The term of 4ax + 3by - 3ay - 4bx can be rearranged and factorized . 4ax - 4bx - 3ay + 3by = 4x(a-b) - 3y(a-b) = (a-b) (4x - 3y) (iii) x3 + y3 + x2y + xy2 = x3 + x2y + xy2 + y3 = x2(x+y) + y2 (x+y) = (x+y) (x2+y2)

Factorise this question -Maths 9th

Description : Factorise this question -Maths 9th

Last Answer : (i) 9x2 + 30xy + 25y2 = (3x2 + 2(3x) (5y) + (5y)2 = (3x + 5y)2 (ii) 9x2 - 30xy + 25y2 = (3x)2 - 2(3x) (5y) + 5y2 = (3x - 5y)2

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Factorise the following : 9x2 -12x+ 3 -Maths 9th

Description : Factorise the following : 9x2 -12x+ 3 -Maths 9th

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Factorise the following : 9x2 +4y2 + 16z2 +12xy-16yz -24xz -Maths 9th

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Last Answer : We know that, a3 + b3 + c3 – 3 abc = (a + b + c)(a2 + b2 + c2 -ab-bc-ca) Also, if a + b + c = 0, then a3 + b3 + c3 = 3abc Here, we see that (x-2y) +(2y-3z)+ (3z-x) = 0 Therefore, (x-2y)3 + (2y-3z)3 + (3z-x)3 = 3(x-2y)(2y-3z)(3z-x).

x^4+x^2+25 factorise this -Maths 9th

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

Factorise each of the following expressions: -Maths 9th

Description : Factorise each of the following expressions: -Maths 9th

Last Answer : (i) 48x3 - 36x2 = 12.4 x2 x - 12.3x2 = 12x2 (4x - 3) (ii) 5x2 - 15xy = 5x (x-3y) (iii) 15x3y2z - 25xy2z3 = 5xy2z(3x2 - 5z2)

Factorise this question -Maths 9th

Description : Factorise this question -Maths 9th

Last Answer : (i) The greatest monomial that is a common factor of the three terms is 6xy. ∴ 30x3y + 24x2y2 - 6xy = 6xy (5x2 + 4xy - 1) (ii) Here the polynomial (a-b) is a common factor. ∴ 5x(a-b) + 6y(a-b) = (a-b) (5x + 6y)

Factorise this question -Maths 9th

Description : Factorise this question -Maths 9th

Last Answer : (i) 7a3 + 7a - 2a2 - 2 = 7a(a2 + 1) - 2 (a2 + 1) = (a2 + 1) (7a - 2) (ii) The term of 4ax + 3by - 3ay - 4bx can be rearranged and factorized . 4ax - 4bx - 3ay + 3by = 4x(a-b) - 3y(a-b) = (a-b) (4x - 3y) (iii) x3 + y3 + x2y + xy2 = x3 + x2y + xy2 + y3 = x2(x+y) + y2 (x+y) = (x+y) (x2+y2)

Factorise this question -Maths 9th

Description : Factorise this question -Maths 9th

Last Answer : (i) 9x2 + 30xy + 25y2 = (3x2 + 2(3x) (5y) + (5y)2 = (3x + 5y)2 (ii) 9x2 - 30xy + 25y2 = (3x)2 - 2(3x) (5y) + 5y2 = (3x - 5y)2

Factorise : x2 + 9x +18 -Maths 9th

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Description : Factorise : 2x3 -3x2 -17x + 30 -Maths 9th

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Factorise the following : 9x2 +4y2 + 16z2 +12xy-16yz -24xz -Maths 9th

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Description : Factorise the following -Maths 9th

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