SOLUTION: Factor Completely 1. 3x^-2x-8 2. 24x^+10x-4 (include the check of your answer using multiplication)(suppose to be factoring the polynomials) 3.2(x+y)^(2)+(x+y)-3

Algebra ->  Equations -> SOLUTION: Factor Completely 1. 3x^-2x-8 2. 24x^+10x-4 (include the check of your answer using multiplication)(suppose to be factoring the polynomials) 3.2(x+y)^(2)+(x+y)-3      Log On


   

Question 116579: Factor Completely
1. 3x^-2x-8
2. 24x^+10x-4
(include the check of your answer using multiplication)(suppose to be factoring the polynomials)
3.2(x+y)^(2)+(x+y)-3
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.3x%5E2-2x-8=%283x%2Ba%29%28x%2Bb%29=3x%5E2%2B%283b%2Ba%29x%2B%28ab%29
ab=-8
3b%2Ba=-2
You can look at all combinations of factors of 8 for a and b to see which ones can actually solve both equations.
Since you have 2 equations and two unknowns, you can create another quadratic equation to solve and find the answer.
We'll do this on number 1 to show how.
b=-8%2Fa
-24%2Fa%2Ba=-2
-24%2Ba%5E2=-2a
a%5E2%2B2a-24=0
%28a%2B6%29%28a-4%29=0
a=-6 and a=4
a=4, b=-2
3x%5E2-2x-8=%283x%2B4%29%28x-2%29
2. 24x%5E2%2B10x-4=%286x%2Ba%29%284x%2Bb%29=24x%5E2%2B%286b%2B4a%29x%2Bab
ab=-4
6b%2B4a=10
a=4%2C+b=-1
24x%5E2%2B10x-4=%286x%2B4%29%284x-1%29
3.+2%28x%2By%29%5E2%2B%28x%2By%29-3
First use a substitution z=x%2By to transform the equation to
+2z%5E2%2Bz-3=%282z%2Ba%29%28z%2Bb%29=2z%5E2%2B%282b%2Ba%29z%2Bab
ab=-3
2b%2Ba=1
a=-3,b=1
2z%5E2%2Bz-3=%282z%2Ba%29%28z%2Bb%29
2z%5E2%2Bz-3=%282z-3%29%28z%2B1%29
2%28x%2By%29%5E2%2B%28x%2By%29-3=%282%28x%2By%29-3%29%28x%2By%2B1%29
2%28x%2By%29%5E2%2B%28x%2By%29-3=%282x%2B2y-3%29%28x%2By%2B1%29