1970 AMC 12 Problem 11

Attempt Problem 11 of the 1970 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 1970 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

11.

If two factors of

2x^3-hx+k

are

x+2

and

x-1,

the value of

|2h-3k|

is:

4

3

2

1

0

Apply the factor theorem at

x=-2

and

x=1

Solve

-16+2h+k=0

and

2-h+k=0

The factor theorem gives

\begin{aligned} -16+2h+k&=0,\\ 2-h+k&=0. \end{aligned}

Subtracting the second equation from the first gives

3h=18,

h=6

and then

k=4.

Hence

|2h-3k|=|12-12|=0.

Therefore, the correct answer is E.

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