Which of the following is a factor of the polynomial below?

Question

asked Aug 3, 2020 103k views

2 Answers

GuRAm · Answer 1 · 2020-08-09T17:25:53+0000

For this case we must indicate which of the options given is a factor of the following polynomial:

4c ^ 3-2c ^ 2-6c

If we take common factor of the terms we have:

2c (2c ^ 2-c-3)

Within the parenthesis we have
2c ^ 2-c-3 , then:

The term of the medium is rewritten as a sum of two terms, whose multiplication is
2 * (- 3) = - 6 and the sum is -1. These numbers are:

-3 and 2

$(-3) (2) = - 6\\-3 + 2 = -1$

So;

$2c ^ 2-c-3 =\\2c ^ 2-3c + 2c-3$

Factoring for each group we have:

c (2c-3) +1 (2c-3)

This is equivalent to:

(c + 1) (2c-3)

Thus,
2c ^ 2-c-3 = (c + 1) (2c-3)

Then,
4c ^ 3-2c ^ 2-6c = 2c ((c + 1) (2c-3))

Thus, a factor of the polynomial is
c + 1

Answer:

Option A