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melomori [17]
2 years ago
11

Will give BRAINLIEST!! Write a polynomial and show all the steps you would take to factor this polynomial completely. Please exp

lain each step thoroughly.
I am not accepting links. Thank you:)
Mathematics
1 answer:
Nikolay [14]2 years ago
3 0

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.

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