Question

2xcube-5xsquare-14x+8​

Answer 1

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Answer 2

Question:

Factorize the following: 2x³ - 5x² - 14x + 8

Answer:

2x³ - 5x² - 14x + 8 = (x + 2)(x - 4)(2x - 1)

Step-by-step explanation:

$p(x) = 2x^3 - 5x^2 - 14x + 8 = 0$

One root has to be found for the factorization of p(x). It seems that -2 is a root of the polynomial.

$p(-2) = 2(-2)^3-5(-2)^2-14(-2)+8 \\ \\ p(-2)=2(-8)- 5(4)-(-28)+8 \\ \\ p(-2)=-16-20+28+8 \\ \\ p(-2)=0$

So (x + 2) is a factor of p(x).

Dividing p(x) by (x + 2),

$2x^3-5x^2-14x+8 \\ \\ 2x^3+4x^2-9x^2-18x+4x+8 \\ \\ 2x^2(x+2)-9x(x+2)+4(x+2) \\ \\ (x+2)(2x^2-9x+4) \\ \\ (x+2)(2x^2-x-8x+4) \\ \\ (x+2)(x(2x-1)-4(2x-1)) \\ \\ (x+2)(x-4)(2x-1)$

$\boxed{\therefore\ 2x^3 - 5x^2 - 14x + 8=(x+2)(x-4)(2x-1)}$