SAT Math : How to factor a trinomial

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #22 : Polynomials

Solve each problem and decide which is the best of the choices given.

 

What are the zeros of the following trinomial?

\(\displaystyle 3x^3-30x^2+63x\)

Possible Answers:

\(\displaystyle x=7,3\)

\(\displaystyle x=3,7,-3\)

\(\displaystyle x=0,-7,-3\)

\(\displaystyle x=0,7,3\)

\(\displaystyle x=-7,-3\)

Correct answer:

\(\displaystyle x=0,7,3\)

Explanation:

First factor out a \(\displaystyle 3x\). Then the factors of the remaining polynomial, 

\(\displaystyle 3x(x^2-10x+21)=0\), are \(\displaystyle (x-7)\) and \(\displaystyle (x-3)\).

Set everything equal to zero and you get \(\displaystyle x=3\), \(\displaystyle x=7\), and \(\displaystyle x=0\) because you cant forget to set \(\displaystyle 3x\) equal to zero.

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