SOLUTION: factor by grouping: 8x^2+18x-35

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: factor by grouping: 8x^2+18x-35      Log On


   



Question 152454: factor by grouping:
8x^2+18x-35

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
factor by grouping:
8x%5E2%2B18x-35

Multiply the 8 by the -35 and get -280
Write down all the pairs of factors of its absolute value,
280:

280%2A1
140%2A2
70%2A4
56%2A5
40%2A7
35%2A8
28%2A10
20%2A14

Now since the LAST SIGN in 8x%5E2%2B18x-35
is MINUS, we SUBTRACT the two 
factors in absolute value:

[Note: If the last term had been PLUS, we 
would have ADDED the two factors in 
absolute value.]

280-1=279
140-2=138
70-4-66
56-5=51
40-7=33
35-8=27
28-10=18
20-14=6

Now we look at the middle term of 8x%5E2%2B18x-35,
which is 18 and we look at the 
list of differences and find the
absolute value of 18 in the next to
last difference, 28-10=18.

So we substitute 28-10 for the 18:

8x%5E2%2B18x-35
8x%5E2%2B%2828-10%29x-35

Now we remove the parentheses by distributing:

8x%5E2%2B28x-10x-35

Factor 4x out of the first two terms
Factor -5 out of the last two terms:

4x%2A%282x%2B7%29-5%282x%2B7%29

Now factor out %282x%2B7%29

%282x%2B7%29%284x-5%29

Edwin