If b and c are constants and (x+2)(x+b)=x^2+cx+6, then c is

1988 AMC 12 Problem 5

Attempt Problem 5 of the 1988 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1988 AMC 12 solutions, or check the answer key.

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b

and

c

are constants and

(x+2)(x+b)=x^2+cx+6,

then

c

-5

-3

-1

3

5

Expand the product on the left

Compare the constant term before comparing the coefficient of

x

Expansion gives

x^2+(b+2)x+2b.

Thus

2b=6,

b=3,

and

c=b+2=5.

Thus the correct answer is E.