So to factor this expression, I'm going to be factoring by grouping. Firstly, what two terms have a sum of 4x and a product of -32x²? That's going to be 8x and -4x. Replace 4x with 8x - 4x:
[tex]x^2+8x-4x-32[/tex]
Now, factor x² + 8x and -4x - 32 separately. Make sure that they have the same quantity on the inside of the parentheses:
[tex]x(x+8)-4(x+8)[/tex]
Now you can rewrite the expression as:
[tex](x-4)(x+8)[/tex]
In short, the two binomial factors are (x - 4) and (x + 8).
Answer:
x-4 and x+8
Step-by-step explanation:
Factoring a quadratic equation of the form x^2+bx+c:
Divide b into two numbers p and q, so that p+q = b and p*q = c
8 + (-4) = 4 = b
8 * (-4) = -32 = c
x^2+8x-4x-32
Factor by grouping
(x^2+8x)+ (-4x-32) =
x*(x+8) + -4* (x+8) = (x-4)(x+8)
