SAT Math : Factoring Equations

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #1991 : Sat Mathematics

Factor 

\(\displaystyle x^3 - 3x^2 - 4x + 12\)

Possible Answers:

\(\displaystyle (x+2)(x-2)(x-3)\)

\(\displaystyle x(x-4)(x+1)\)

cannot be factored

\(\displaystyle (x-2)^2(x-3)\)

\(\displaystyle (x^3-4x)(12-3x^2)\)

Correct answer:

\(\displaystyle (x+2)(x-2)(x-3)\)

Explanation:

This expression can be factored by grouping. 

xcan be factored out of the first two terms. 

\(\displaystyle x^2(x-3)-4x+12\)

-4 can be factored out of the second two terms. 

\(\displaystyle x^2(x-3)-4(x-3)\)

Now we can factor out the term (x-3). 

\(\displaystyle (x-3)(x^2-4)\)

x- 4 is a difference of squares. It can be factored into (x + 2)(x - 2). 

\(\displaystyle (x-3)(x+2)(x-2)\)

 

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