Question 1

Which of the following is a binomial?

Accepted Answer

$$x^2 + 3x$

Question 2

What is the degree of the polynomial $$4x^3$$ + $$2x^2 - 7x + 8$?

Accepted Answer

$$3$$

Question 3

Add the polynomials $$2x^2 + 6x - 1$ and 3x^2$ + 2x - 2.$$

Accepted Answer

$$5x^2 + 8x - 3$

Question 4

Subtract $$x^2 + 2x - 3$ from 3x^2$ + 6x - 2.$$

Accepted Answer

$$2x^2 + 4x + 1$

Question 5

Multiply $$(3x)(x+4).$$

Accepted Answer

$$3x^2 + 12x$

Question 6

Which of the following is the result of $$(x+2)(3x-4)$$ using the FOIL method?

Accepted Answer

$$3x^2 + 2x - 8$

Question 7

What is the factored form of $$x^2 - 25$?

Accepted Answer

$$(x+5)(x-5)$$

Question 8

Which of the following is a perfect square trinomial?

Accepted Answer

$$x^2 + 10x + 25$

Question 9

Divide $$x^2 - 5x + 21$ by x - 3$ using long division. What is the quotient?

Accepted Answer

$$x - 2$$

Question 10

Factor $$2x + 4$$ completely.

Accepted Answer

$$2(x + 2)$$

Question 11

What is the greatest common factor (GCF) of $$6x^2$$ and $$9x$$?

Accepted Answer

$$3x$$

Question 12

Factor $$x^2 + 6x + 9$.

Accepted Answer

$$(x + 3)^2$

Question 13

Which of the following is the correct factorization of $$x^2 + 10x + 21$?

Accepted Answer

$$(x + 7)(x + 3)$$

Question 14

Factor $$x^2 + 12x + 36$.

Accepted Answer

$$(x + 6)^2$

Question 15

Which of the following is the correct factorization by grouping for $$x^3$$ + $$2x^2 + x + 2$?

Accepted Answer

$$(x^2 + 1)(x + 2$$)$$

Question 16

Factor $$x^3 - 8$ as a difference of cubes.

Accepted Answer

$$(x - 2)(x^2$ + 2x + 4)$$

Question 17

Using the slide and divide method, what is the factorization of $$2x^2 + 7x + 3$?

Accepted Answer

$$(2x + 1)(x + 3)$$

Question 18

Which of the following is the correct factorization for $$x^2 - 4x + 4$?

Accepted Answer

$$(x - 2)^2$

Question 19

A rectangular garden has an area represented by $$x^2 + 6x + 9$ square meters. What are the possible dimensions of the garden?

Accepted Answer

$$(x + 3)$$ meters by $$(x + 3)$$ meters

Polynomials: Operations and Factoring – Precalculus Study Notes

Study Guide - Practice Questions