Question 1

Which of the following is the correct definition of the Greatest Common Factor (GCF) when factoring polynomials?

Accepted Answer

The GCF is the largest factor that divides all terms of the polynomial, including both coefficients and variables with the smallest exponent present in all terms.

Question 2

Factor the polynomial $6a^2 + 27$ completely.

Accepted Answer

$3(2a^2 + 9)$

Question 3

Which of the following polynomials is considered 'prime' (cannot be factored further using integer coefficients)?

Accepted Answer

$5x - 13y$

Question 4

A chemist is mixing two solutions, represented by $12c^2 - 20d^2$. What is the factored form using the GCF?

Accepted Answer

$4(3c^2 - 5d^2)$

Question 5

Factor the polynomial $18x^2yz - 24xz^2 + 36yz^3$ completely.

Accepted Answer

$6z(3x^2y - 4xz + 6yz^2)$

Question 6

Which of the following is the correct first step when factoring $8m^2n^2 - 24mn^3 + 16mn$?

Accepted Answer

Factor out $mn$ as the GCF.

Question 7

A company’s profit is modeled by $15a^2b - 30ab$. Factor this expression completely.

Accepted Answer

$15ab(a - 2)$

Question 8

Which of the following is the correct factored form of $16x^6y + 16x^2y^4 + 32x^3y^2$?

Accepted Answer

$16x^2y(x^4 + 2x y^2 + y^3)$

Question 9

A biologist is analyzing the growth of bacteria, modeled by $9r^3s^2 - 30rs^3$. What is the factored form using the GCF?

Accepted Answer

$3rs^2(3r^2 - 10s)$

Question 10

Which of the following is the correct factored form of $12a^5b^2 - 36a^4b^3 - 6a^2b^2$?

Accepted Answer

$6a^2b^2(2a^3 - 6a^2b - 1)$

Question 11

Factor the polynomial $7y - 7$ completely.

Accepted Answer

$7(y - 1)$

Question 12

A physics equation is given as $81m + 48mn$. What is the factored form using the GCF?

Accepted Answer

$3(27m + 16mn)$

Question 13

Which of the following is the correct factored form of $14gh^2 + 28gh + 14h$?

Accepted Answer

$14h(g h + 2g + 1)$

Question 14

A business’s cost function is $36ab^2 - 48a^2b$. Factor this expression completely.

Accepted Answer

$12ab(3b - 4a)$

Question 15

Which of the following is the correct factored form of $x^2y + 3xy$?

Accepted Answer

$xy(x + 3)$

Question 16

A medical researcher models a dosage as $10x^3y^2 - 2xy^2 + 14xy$. What is the factored form using the GCF?

Accepted Answer

$2xy(5x^2y - 1y + 7)$

Question 17

Which of the following is the correct factored form of $ab - a$?

Accepted Answer

$a(b - 1)$

Question 18

A factory produces widgets modeled by $35a^2 - 20ab^2 + 15a$. What is the factored form using the GCF?

Accepted Answer

$5a(7a - 4b^2 + 3)$

Question 19

Which of the following is the correct factored form of $x^3y^2 + x^2y + x$?

Accepted Answer

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

Question 20

A student is asked to factor $64 - 40ab$. What is the correct factored form using the GCF?

Accepted Answer

$8(8 - 5ab)$

Factoring Polynomials Using the Greatest Common Factor (GCF)

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