Question

Explain, in complete sentences, how you would completely factor 20x2 – 28x – 48 and check your factors for accuracy.

Answer 1

Extract a 4 from each term, getting 4(5x2-7x-12) That leaves the 5x2-7x-12 to factor if possible. It is going to look like (a + b) (c +d) if it is factorable. ab is easy a 5 is prime and it is positive (5x + b)(x + d) The product bd is -12 so that means there will be unlike signs. We also know that the possible factors of -12 are (12,1)(6,2), and (4,3) with their signs being different. Doe this make sense so far?

Answer 2

To which pair of factors we must consider the -7x term in the expression, and this is why:
The sum of the factors of the -12 with one being multiplied by the 5 (which was a) must equal the -7. So lets see which one it is. (5*1)and -12 would get it as -12 + 5 =-7
So now the factors are 4(x + 1)(5x - 12).

Answer 3

You can then multiply this out {4(x+1)(5x-12)} and get the original expression to verify correct factoring.

Answer 4

Thank you