Question

Find Factors of 2x ^3 + 5x ^2 - 11x +4

Answer 1

Answer:

$\Large\boxed{(X-1)(2x-1)(X+4)}$

Step-by-step explanation:

Given:

Find the factors of 2x³+5x²-11x+4

Solutions:

First, you used rational root theorem formula.

$\Large\boxed{\textnormal{RATIONAL ROOT THEOREM FORMULA}}}$

$\displaystyle A_0=4$

$\displaystyle A_N=2$

$\displaystyle A_0=1, 2, 4$

$\displaystyle A_N= 1,2$

Rational numbers are:

$\displaystyle \pm \frac{1,\:2,\:4}{1,\:2}$

Factors of x-1.

$\displaystyle (x-1)\frac{2x^3+5x^2-11x+4}{x-1}$

$\displaystyle \frac{2x^3+5x^2-11x+4}{x-1}=2x^2+7x-4$

Solve.

Factor it out.

$\displaystyle 2x^2+7x-4$

$\displaystyle \left(2x^2-x\right)+\left(8x-4\right)$

Factor it out by the x of 2x²-x.

$\Large\boxed{\textnormal{EXPONENT RULES}}$

$\displaystyle A^B^+^C=A^BA^C$

$\displaystyle XX=X^2$

$\displaystyle 2XX-X$

Common term of x.

$\displaystyle \boxed{X(2x-1)}$

Factor it out by the 4 of 8x-4.

Multiply.

$\displaystyle 2*4=8$

Common term of 4.

$\displaystyle 4(2x-1)$

$\displaystyle x\left(2x-1\right)+4\left(2x-1\right)$

Common term of 2x-1.

$\displaystyle \boxed{(2x-1)(x+4)}$

$\Large\boxed{(X-1)(2x-1)(X+4)}$

Hence, the correct answer is (x-1)(2x-1)(x+4).