SOLUTION: if the factorised form of (x+2)^2 + b(x+2) + a is (x+6)(x+1) then find a and b

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Question 1152320: if the factorised form of (x+2)^2 + b(x+2) + a is (x+6)(x+1) then find a and b
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!



+%28x%2B2%29%5E2+%2B+b%28x%2B2%29+%2B+a+=+%28x%2B6%29%28x%2B1%29+

Expand both sides:

+%28x%5E2%2B4x%2B4%29+%2B+%28bx%2B2b%29+%2B+a+=++x%5E2%2B7x%2B6+



Collect like terms on LHS:

+%28x%5E2%29+%2B+%28b%2B4%29x+%2B+%282b%2Ba%2B4%29+=++x%5E2%2B7x%2B6+



Now compare coefficents of x%5E2,x%5E1, x%5E0 terms from LHS and RHS:



+b%2B4+=+7+

+2b%2Ba%2B4+=+6+



Solve for a and b:  +highlight%28+a=-4+%29, highlight%28+b=3+%29



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Check:

+x%5E2%2B4x%2B4+%2B+3%28x%2B2%29+%2B+%28-4%29+ =

+x%5E2%2B4x%2B4+%2B+3x%2B6+-4+ = 

+x%5E2%2B7x%2B6+ =

+%28x%2B6%29%28x%2B1%29+  (ok)