Math Core

This test covers polynomial operations, polynomial division, the remainder and factor theorems, solving polynomial equations, the fundamental theorem of algebra, and graphing polynomial functions.

Question 1

Multiply $(x - 2)(3x^2 + x - 4)$ . What is the coefficient of $x^2$ in the result?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 2

Simplify $(5x^3 - x + 2) - (2x^3 + 3x^2 - x - 4)$ .

Question 3

Divide $x^3 + 2x^2 - 5x + 1$ by $x - 2$ .

Question 4

Divide $2x^3 - x^2 + 3x - 1$ by $x^2 + 1$ .

Question 5

Find the remainder when $3x^4 - 2x^2 + x - 5$ is divided by $x + 2$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 6

Find $k$ so that $x + 3$ is a factor of $x^3 + 4x^2 + kx - 6$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 7

Solve $x^4 - 10x^2 + 9 = 0$ .

Separate answers with commas, e.g. 2, -5

Question 8

Solve $2x^3 - 5x^2 - 4x + 3 = 0$ .

Separate answers with commas, e.g. 2, -5

Question 9

Find all real solutions of $x^3 - 5x^2 - 3x + 15 = 0$ .

Separate answers with commas, e.g. 2, -5

Question 10

Find all complex solutions of $x^3 - 1 = 0$ .

Question 11

How many complex zeros, counted with multiplicity, does $(x^2 - 4)^3$ have?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 12

A cubic $P(x) = x^3 + bx^2 + cx + d$ has real coefficients, and two of its zeros are $4i$ and $1$ . Find $d$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 13

Describe the end behavior of $f(x) = -x^4 + 3x$ .

Question 14

How does the graph of $f(x) = (x + 2)^3(x - 1)^2$ behave at its two $x$ -intercepts?

Question 15

Which function has this graph?

y = -(x + 1)*(x - 2)*(x - 4)(-1, 0)(2, 0)(4, 0)(0, -8)Open in grapher →