Question

Will give BRAINLIEST!! Write a polynomial and show all the steps you would take to factor this polynomial completely. Please explain each step thoroughly.
I am not accepting links. Thank you:)

Answer 1

Step-by-step explanation:

Consider this polynomial,

$8 {x}^{2} + 2x - 3$

First, I do the AC memethod. To find my two numbers,

That is to find two numbers that multiplied will equal my leading coeffeicent, A times my constant, C

And that will also add to 2, my middle term.

So using that

$8 \times - 3 = - 24$

So let find factors of-24:

Factors can be positve or negative

The factors of 24 are : 1,2,3,4,6 8,12,24.

So which one of these add up to 2.

$6 + ( - 4) = 2$

and

$6 \times - 4 = - 24$

So six and negative four is our numbers.

Now, let set up our binomials

Step 1: Rewrite the orginal equation by using 6x and -4x instead of 2x.

Disclaimer: The placement of these numbers doesn't matter.

So we have

$8 {x}^{2} + 6x - 4x - 3$

Step 2: Group the first two terms and last two terms

$(8 {x}^{2} + 6x) + ( - 4x - 3)$

Factors the first group by finding the GCF.

x is the greatest common variable, and 2 is the gcf so we have

$2x(4x + 3) + ( - 4x - 3)$

Next, factor the next group by -1.

$2x(4x + 3) - 1(4x + 3)$

Combine the outside factors.

$(2x - 1)(4x + 3)$

So those are the factors.