1957 AMC 12 Problem 4

Attempt Problem 4 of the 1957 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 1957 AMC 12 solutions, or check the answer key.

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

The first step in finding the product

(3x+2)(x-5)

by use of the distributive property in the form

a(b+c)=ab+ac

is:

3x^2-13x-10

3x(x-5)+2(x-5)

(3x+2)x+(3x+2)(-5)

3x^2-17x-10

3x^2+2x-15x-10

Match the second factor with

b+c

in the stated form

Take

a=3x+2,

b=x,

and

c=-5

Using the property in precisely the stated form, set

a=3x+2,

b=x,

and

c=-5.

Then

\begin{gathered} (3x+2)(x-5)\\ =(3x+2)x+(3x+2)(-5). \end{gathered}

Thus, the correct answer is C.

Problem 4 in other years