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PSAT Math : How to factor a trinomial

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Example Questions

Example Question #1 : How To Factor A Trinomial

Factor the following expression completely:

$\displaystyle x^4-8x^3+12x^2$

Possible Answers:

$\displaystyle x^2(x+6)(x+2)$

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

$\displaystyle x^2(x-6)(x-2)$

$\displaystyle x^2(x+3)(x+4)$

$\displaystyle x^2(x^2-8x+12)$

Correct answer:

$\displaystyle x^2(x-6)(x-2)$

Explanation:

We must begin by factoring out x^2 $\displaystyle x^2$ from each term.

$\displaystyle x^2(x^2-8x+12)$

Next, we must find two numbers that sum to $\displaystyle -8$ and multiply to $\displaystyle 12$ .

$\displaystyle (-6)+(-2)=-8$

$\displaystyle -6*-2=12$

Thus, our final answer is:

$\displaystyle x^2(x-6)(x-2)$

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Example Question #2 : Trinomials

Factor the following trinomial:

$\displaystyle x^2-x-12$

Possible Answers:

$\displaystyle (x+3)(x-4)$

$\displaystyle (x-3)(x-4)$

$\displaystyle (x-1)(x-12)$

$\displaystyle (x-6)(x+2)$

$\displaystyle (x+4)(x-3)$

Correct answer:

$\displaystyle (x+3)(x-4)$

Explanation:

$\displaystyle x^2-x-12$

To trinomial is in ax+bx+c $\displaystyle ax+bx+c$ form

In order to factor, find two numbers whose procuct is $\displaystyle c$ , in this case $\displaystyle -12$ , and whose sum is $\displaystyle b$ , in this case $\displaystyle -1$

Factors of $\displaystyle -12$ :

$\displaystyle -1, 12; 1, -12; -3,4; 3,-4;-2,6; 2,-6$

Which of these pairs has a sum of $\displaystyle -1$ ?

$\displaystyle 3$ and $\displaystyle -4$

Therefore the factored form of $\displaystyle x^2-x-12$ is:

$\displaystyle (x+3)(x-4)$

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Example Question #41 : Variables

Factor the trinomial.

$x^{2}-5x-14$ $\displaystyle x^{2}-5x-14$

Possible Answers:

$\displaystyle (x+7)(x-2)$

$\displaystyle (x-8)(x+3)$

$\displaystyle (x-7)(x+2)$

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

Correct answer:

$\displaystyle (x-7)(x+2)$

Explanation:

Our factors will need to have a product of (-14) $\displaystyle (-14)$ , and a sum of (-5) $\displaystyle (-5)$ , so our factors must be (-7) $\displaystyle (-7)$ and $\displaystyle 2$ .

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PSAT Math : How to factor a trinomial

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #1 : How To Factor A Trinomial

Example Question #2 : Trinomials

Example Question #41 : Variables

All PSAT Math Resources

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