SOLUTION: Find the constants a and b such that x^2+4*x+a=(x+1)*(x+b)

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Question 862552: Find the constants a and b such that x^2+4*x+a=(x+1)*(x+b)
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Hint: Corresponding Positions.

Right-hand side is x%5E2%2Bx%2Bbx%2Bb=x%5E2%2B%281%2Bb%29x%2Bb.
Original left side then means x%5E2%2B4x%2Ba=x%5E2%2B%281%2Bb%29x%2Bb.
Use the hint.
Done???
"No".

Trying a little more thoroughly,
x%5E2%2B4%2Ax%2Ba=%28x%2B1%29%2A%28x%2Bb%29 was given.
x%5E2%2B4x%2Ba=x%5E2%2Bx%2Bbx%2Bb
highlight_green%28x%5E2%2B4x%2Ba=x%5E2%2B%281%2Bb%29x%2Bb%29.
Now, these are two equal quadratic expressions. Both expressions are arranged in decreasing powers of x. Coefficients in corresponding positions are equal.