SOLUTION: Find the constants a and b such that: {x^2−2x+a = ( x +3 )( x + b )}

Question 1144103: Find the constants a and b such that:
{x^2−2x+a = ( x +3 )( x + b )}

Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x^2 - 2x + a = (x + 3) * (x + b)
simplify the right side of this equation to get:
x^2 - 2x + a = x^2 + bx + 3x + 3b
combine like terms on the right sides of this equation to get:
x^2 - 2x + a = x^2 + (b + 3)x + 3b
for the expressions on both sides of this equation to be equal, .....
x^2 must be equal to x^2 and -2x must be equal to (b + 3)x and a must be equal to 3b.
if -2x = (b+3)x, then -2 must be equal to b + 3 resulting in b = -5.
if b = -5 and a = 3b, then a must be equal to -15.
your solution appears to be a = -15 and b = -5
the original equation becomes x^2 - 2x - 15 = (x + 3) * (x - 5).
simplify the right sides of this equation to get x^2 - 2x - 15 = x^2 - 2x - 15.
this, i believe, confirms the solution is correct.
your solution is that a = -15 and b = -5 as best i can determine.

Answer by greenestamps(13208) (Show Source): You can put this solution on YOUR website!

Expand the expression on the right and combine like terms

The coefficients of the linear terms have to be equal:

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And the linear terms also have to be equal, so

ANSWERS: a=-15; b=-5
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