SOLUTION: Factor completely. 49a^2+4-28a

Question 330746: Factor completely. 49a^2+4-28a
Answer by neatmath(302) (Show Source): You can put this solution on YOUR website!

We must use the factors of the first term to see how this can be factored, using either 49 and 1, or 7 and 7.

or

Notice that both factors must have a negative sign in them, since the last term is positive, but the middle term is negative.

Then we just have to use the factors of 4 to see what numbers will work to factor this.

This is just a matter of guessing and checking, or trial and error. Factors of 4 are 4 and 1, or 2 and 2. So our answer MUST be one of the following, if this polynomial is factorable:

or or or

or

Upon closer inspection, we can see that:

does indeed multiply out to

so the answer is

This polynomial is a special one, in the form of:

where and

Factoring polynomials is hard, and it takes a lot of practice. There are also different ways to approach this problem, but I hope this helps!
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