SAT Practice Test - Math - Polynomials

SAT practice tests arranged by topic and difficulty level. In this section find tips and tactics for solving questions that focus on Polynomials.

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SAT 2015 Test. For a polynomial p(x), the value of p(3) is -2. Which of the following must be true about p(x)?
A) x-5 is a factor of p(x).
B) x-2 is a factor of p(x).
C) x+2 is a factor of p(x).
D) The remainder when p(x) is divided by x-3 is −2.

Answer:

 If the polynomial p(x) is divided by x-3, the result can be written as

$\frac{p(x)}{x-3}=q(x)+\frac{r}{x-3}$

$p(x)=(x-3)q(x)+r$

where q(x) is a polynomial and r is the remainder (in this case, r is a real number, since x-3 is a degree 1 polynomial).

It is given that $p(3)=-2$:

$p(x)=(x-3)q(x)+r$
$p(3)=(3-3)q(3)+r$
$-2=(0)q(3)+r$
$-2=r$

Answer: D

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SAT Practice Test. The function f is defined by $f(x)=2x^3+3x^2+cx+8$, where c is a constant. In the x y plane, the graph of f intersects the x axis at the three points (-4, 0), (1/2, 0), and (p, 0). What is the value of c?
A. -18
B. -2
C. 2
D. 10

Answer:

If (-4, 0) is one solution, lt's solve for c, substituting -4 for x and 0 for y:
$f(x)=2x^3+3x^2+cx+8$
$0=2(-4)^3+3(-4)^2+c(-4)+8$
$0=-2.64+3.16-4c+8$
$4c=-72$
$c=-18$

Answer: A

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