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Sagot :
Step-by-step explanation:
Consider this polynomial,
[tex]8 {x}^{2} + 2x - 3[/tex]
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
[tex]8 \times - 3 = - 24[/tex]
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.
[tex]6 + ( - 4) = 2[/tex]
and
[tex]6 \times - 4 = - 24[/tex]
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
[tex]8 {x}^{2} + 6x - 4x - 3[/tex]
Step 2: Group the first two terms and last two terms
[tex](8 {x}^{2} + 6x) + ( - 4x - 3)[/tex]
Factors the first group by finding the GCF.
x is the greatest common variable, and 2 is the gcf so we have
[tex]2x(4x + 3) + ( - 4x - 3)[/tex]
Next, factor the next group by -1.
[tex]2x(4x + 3) - 1(4x + 3)[/tex]
Combine the outside factors.
[tex](2x - 1)(4x + 3)[/tex]
So those are the factors.
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