Question

What are the linear factors of the function f(x)=4x3−4x2−11x+6?

Select each correct answer.


(2x−3)

(2x+1)

(x−2)

(x+2)

(2x−1)

(2x+3)

Answer 1

Answer:

(x-2),(2x+3), and (2x-1)

Step-by-step explanation:

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Answer 2

One of the ways of getting the factors of a polynomial is by factorization.

The linear factors of $\mathbf{f(x) = 4x^3 - 4x^2 - 11x + 6}$ are $\mathbf{(2x -1),\ (2x + 3) \ and\ (x - 2)}$

The function is given as:

$\mathbf{f(x) = 4x^3 - 4x^2 - 11x + 6}$

Expand

$\mathbf{f(x) = 4x^3 - 2x^2 - 2x^2 - 12x + x + 6}$

Rewrite as:

$\mathbf{f(x) = 4x^3 -2x^2 -12x - 2x^2 + x + 6}$

Factorize

$\mathbf{f(x) = 2x(2x^2 - x - 6)-1(2x^2 - x - 6)}$

Factor out $\mathbf{(2x^2 - x - 6)}$

$\mathbf{f(x) = (2x -1)(2x^2 - x - 6)}$

Expand

$\mathbf{f(x) = (2x -1)(2x^2 -4x + 3x - 6)}$

Factorize

$\mathbf{f(x) = (2x -1)(2x(x -2) + 3(x - 2)}$

Factor out x -2

$\mathbf{f(x) = (2x -1)(2x + 3) (x - 2)}$

Hence, the linear factors are: $\mathbf{(2x -1),\ (2x + 3) \ and\ (x - 2)}$

Read more about linear factors at:

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