SOLUTION: Express 2x^2 +3x in the form ax(x + 1) + b(x + 1) + c

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Question 1121715: Express 2x^2 +3x in the form ax(x + 1) + b(x + 1) + c
Found 2 solutions by Boreal, greenestamps:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
expanding the second expression
ax^2+ax+bx+b+c
2x^2+2x+x+1-1
2x(x+1)+1(x+1)-1

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Expand the expression on the right and equate the coefficients of each power of x.

2x%5E2%2B3x+=+ax%5E2%2Bax%2Bbx%2Bb%2Bc
2x%5E2%2B3x%2B0+=+ax%5E2%2B%28a%2Bb%29x%2B%28b%2Bc%29

So we need to have
a=2
a+b=3
b+c=0

That system is easily solved: a=2, b=1, c=-1. So

2x^2+3x = 2x(x+1)+1(x+1)-1