Question

Factorize 2x^3-x^2-15x+18 in synthetic division method

Answer 1

Answer:

Here x = 2 is zero of polynomial (by hit & trial) so (x - 2) is one factor. Now

$2 {x}^{3} - {x}^{2} - 15x + 18 = 2 {x}^{3} - 4 {x}^{2} + 3 {x}^{2} - 6x - 9x + 18 =$

$2 {x}^{2} (x - 2) + 3x(x - 2) - 9(x - 2) = (x - 2)(2 {x}^{2} + 3x - 9)$

$(x - 2)(2 {x}^{2} + 6x - 3x - 9) =$

$(x - 2)(2x(x + 3) - 3(x + 3)) =$

$(x - 2)(x + 3)(2x - 3)$

Required factor.

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Answer 2

Answer:

Here x = 2 is zero of polynomial (by hit & trial) so (x - 2) is one factor. Now

2 {x}^{3} - {x}^{2} - 15x + 18 = 2 {x}^{3} - 4 {x}^{2} + 3 {x}^{2} - 6x - 9x + 18 =2x

3

−x

2

−15x+18=2x

3

−4x

2

+3x

2

−6x−9x+18=

2 {x}^{2} (x - 2) + 3x(x - 2) - 9(x - 2) = (x - 2)(2 {x}^{2} + 3x - 9)2x

2

(x−2)+3x(x−2)−9(x−2)=(x−2)(2x

2

+3x−9)

(x - 2)(2 {x}^{2} + 6x - 3x - 9) =(x−2)(2x

2

+6x−3x−9)=

(x - 2)(2x(x + 3) - 3(x + 3)) =(x−2)(2x(x+3)−3(x+3))=

(x - 2)(x + 3)(2x - 3)(x−2)(x+3)(2x−3)

Required factor.

Hope this will help you. Pls mark BRAINLIEST. Thanks