Question 1

Which pair of numbers can be used to factor $x^2 + 18x + 81$?

Accepted Answer

$9$ and $9$

Question 2

What is the factored form of $x^2 - 13x + 40$?

Accepted Answer

$(x - 5)(x - 8)$

Question 3

Given $x^2 + 3x - 54$, which two numbers multiply to $-54$ and add up to $3$?

Accepted Answer

$9$ and $-6$

Question 4

What is the greatest common factor (GCF) of $5x^2 + 75x + 270$?

Accepted Answer

$5$

Question 5

Factor completely: $-4x^2 - 44x + 104$.

Accepted Answer

$-4(x^2 + 11x - 26)$

Question 6

Which is the correct factorization of $x^2 - 2x - 35$?

Accepted Answer

$(x - 7)(x + 5)$

Question 7

A chemical reaction produces a quadratic equation for concentration: $c^2 + 6c + 8 = 0$. What are the possible concentrations?

Accepted Answer

$-2$ and $-4$

Question 8

What is the GCF of $5x^3 + 55x^2 + 120x$?

Accepted Answer

$5x$

Question 9

A projectile's height is modeled by $h(t) = t^2 - 11t + 30$. At what times does the projectile hit the ground?

Accepted Answer

$t = 5$ and $t = 6$

Question 10

Which is the correct factorization of $m^2 + 9m + 18$?

Accepted Answer

$(m + 6)(m + 3)$

Question 11

A business's profit is modeled by $P(x) = x^2 + 4x - 12$. For which values of $x$ does the profit become zero?

Accepted Answer

$x = -6$ and $x = 2$

Question 12

What is the factored form of $a^2 + 4a + 3$?

Accepted Answer

$(a + 3)(a + 1)$

Question 13

Which is the correct factorization of $x^2 - 7x + 12$?

Accepted Answer

$(x - 3)(x - 4)$

Question 14

A quadratic equation $x^2 + 13x + 24$ models the number of bacteria in a culture. What are the possible values for $x$?

Accepted Answer

$-12$ and $-1$

Question 15

What is the GCF of $2x^2 + 24x + 22$?

Accepted Answer

$2$

Question 16

Which pair of numbers can be used to factor $x^2 + 6x + 8$?

Accepted Answer

$2$ and $4$

Question 17

A quadratic equation $x^2 + 4x - 12$ models the height of a ball. What are the roots?

Accepted Answer

$x = -6$ and $x = 2$

Question 18

Which is the correct factorization of $x^2 + 14x + 49$?

Accepted Answer

$(x + 7)^2$

Question 19

A quadratic equation $x^2 - 3x - 54$ models the number of patients in a hospital. What are the possible values for $x$?

Accepted Answer

$x = 9$ and $x = -6$

Factoring Quadratic Expressions and Greatest Common Factor (GCF): Precalculus Study Notes

Study Guide - Practice Questions