Question

Explain, in complete sentences, how to factor 4x^2 – 4x – 48. Explain how your factors could be checked for accuracy.

Answer 1

it is often easier to work with polynomials that are of the for
x^2 + bx +c

so we start our solution process by dividing the polynomial by 4 to obtain
x^2 -x -12

we have a=1, b=-1 and c=-12

write down all possible ways to factor c
in this case it would be
-12 , 1
12 , -1
-6, 2
6 , -2
-4, 3
4, -3

look for the factors which add to be equal to the value of b
in this case -1

-12 + 1 = -11 NOPE
12 + (-1) = 11 NOPE
-6 +2 = -4 NOPE
6 + (-2) = 4 NOPE
-4 + 3 = -1 YES

the solution is (x-4)(x+3)
the solution can be verified (x-4)(x+3) which would give us the original polynomial