Question

Urgent! Will award brainliest... Factor the following polynomial: 0" id="TexFormula1" title="3a^{2}-21a+30" alt="3a^{2}-21a+30" align="absmiddle" class="latex-formula">

Answer 1

Answer:

$3 (a-2) (a-5)$

Step-by-step explanation:

The first step is to find the GCF. Here, it's 3.

$3(a^2-7a+10)$

Then, you factor the polynomial in the parenthesis.

To find the factors, you will need to find 2 numbers that add to -7, and multiply to 10. -2 and -5 add to -7 and multiply to 10. Now, replace -7a with the factors.

$a^2-2a-5a+10$

This of this polynomial as 2 problems.

$a^2-2a$        $-5a+10$

Then, factor again.

$a^2-2a$        $-5a+10$

$a(a-2)$       $-5(a-5)$

Then, you keep the factors in parenthesis, and combine the numbers on the outside.

$(a-2)(a-5)(a-5)$

Since, there are 2 of the same factor, you only need one.

$(a-2)(a-5)$

BUT REMEMBER!! In the very beginning, we had a 3 that we took out, we STILL need to add that to the final answer. The final answer is:

$3 (a-2) (a-5)$