Question

Select the correct answer.

Which expression in factored form is equivalent to this expression?

4(x2 – 2x) – 2(x2 – 3)

A. (2x − 3)(x + 1)

B. 2(x + 1)(x + 3)

C. (2x + 3)(x + 1)

D. 2(x - 1)(x – 3)



Took the test. This is the answer.

Answer 1

Answer:

D. 2(x - 1)(x – 3)

Step-by-step explanation:

4(x2 – 2x) – 2(x2 – 3)

We would first of all expand the expression given

This becomes

= 4x2 - 8x - 2x2 + 6

Rearrange to enable us simplify

4x2 - 2x2 - 8x + 6

= 2x2 - 8x + 6

Factorize

2 (x2 - 4x + 3)

factorizing further using the factors of 3 that add up to -4

2(x2 - x - 3x + 3)

pick out the common factors

2(x(x-1) -3(x-1)

2(x-1)(x-3)

Option D. 2(x - 1)(x – 3) is right

Answer 2

Using the Factor Theorem, the factored form equivalent to this expression is:

$2(x - 1)(x - 3)$, given by option D.

The Factor Theorem states that a polynomial function with roots $x_1, x_2, \codts, x_n$ is given by:

$f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)$

• In which a is the leading coefficient.

In this problem, the expression is:

$4(x^2 - 2x) - 2(x^2 - 3) = 0$

$4x^2 - 8x - 2x^2 + 6 = 0$

$2x^2 - 8x + 6 = 0$

Which is a quadratic equation with coefficients $a = 2, b = -8, c = 6$.

Hence:

$\Delta = b^2 - 4ac = (-8)^2 - 4(2)(6) = 16$

$x_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{8 + 4}{4} = 3$

$x_2 = \frac{-b - \sqrt{\Delta}}{2a} = \frac{8 - 4}{4} = 1$

Hence, the expression is:

$2(x - 1)(x - 3)$, given by option D.

You can learn more about the Factor Theorem at https://brainly.com/question/24380382