Math Core

This test covers all of the Polynomials and Factoring unit: describing, adding and subtracting polynomials, multiplying polynomials, special products, factoring out the GCF, factoring $x^2 + bx + c$ and $ax^2 + bx + c$ , and factoring special cases.

Question 1

What is the degree of $6x^2 - x^5 + 3$ ?

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

Question 2

Find $(4x^2 - 3x + 7) - (x^2 + 2x - 5)$ .

Question 3

When $(2x + 5)(x - 4)$ is multiplied out and simplified, what is the coefficient of $x$ ?

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

Question 4

Find $(x + 2)(x^2 - x + 3)$ .

Question 5

Expand $(3x - 5)^2$ .

Question 6

Use a special product to compute $57 \cdot 63$ .

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

Question 7

Factor $15x^3 - 10x^2$ completely.

Question 8

The trinomial $x^2 - 3x - 28$ factors as $(x + a)(x + b)$ . Find $a$ and $b$ .

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

Question 9

Factor $x^2 - 12x + 35$ .

Question 10

Factor $3x^2 + 10x - 8$ .

Question 11

The trinomial $4x^2 + 4x - 3$ factors as $(2x + 3)(2x + m)$ . What is $m$ ?

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

Question 12

Factor $25x^2 - 36$ .

Question 13

Factor $5x^3 - 20x^2 + 20x$ completely.

Question 14

For what negative value of $k$ is $x^2 + kx + 49$ a perfect square trinomial?

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

Question 15

Factor $x^3 + 3x^2 - 4x - 12$ completely.