SOLUTION: Factor the following into the product of two binomials by “reverse FOIL” method. Then, confirm your answer is correct by multiplying the two binomials: x2 + 8x + 7

Algebra ->  Distributive-associative-commutative-properties -> SOLUTION: Factor the following into the product of two binomials by “reverse FOIL” method. Then, confirm your answer is correct by multiplying the two binomials: x2 + 8x + 7       Log On


   

Question 104668: Factor the following into the product of two binomials by “reverse FOIL” method. Then, confirm your answer is correct by multiplying the two binomials:
x2 + 8x + 7
Answer by HyperBrain(694) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+%2B+8x+%2B+7
I want you to know the shortcut of this method. So, please access my lesson "Factoring trinomials: SHORTCUT!!!" then go back to this page.

Using the quadratic formula,

___________________x=%28-8%2B-sqrt%288%5E2-4%2A1%2A7%29%29%2F%282%2A1%29__________________________
___________________x=%28-8%2B-sqrt%2864-28%29%29%2F%282%29________________________________
___________________x=%28-8%2B-sqrt%2836%29%29%2F%282%29_)_________________________________
___________________x=%28-8%2B-+6%29%2F%282%29_________________________________________
_______________x=-4%2B3 or x=-4-3_____________________________________
_________________x=-1 or x=-7_______________________________________
If x=-1,x+1=0.
If x=-7,x+7=0.
Thus, these are the factors so,
x%5E2+%2B+8x+%2B+7=%28x%2B1%29%2A%28x%2B7%29
Check:
%28x%2B1%29%2A%28x%2B7%29=%28x%2A%28x%2B7%29%29%2B%281%2A%28x%2B7%29%29
___________=%28x%5E2%2B7x%29%2B%28x%2B7%29
___________=x%5E2%2B%287x%2Bx%29%2B7
___________=x%5E2+%2B8x+%2B7
Thus, my lesson is correct and and the resulting answer are also correct!

Power up,
HyperBrain!