Question 1

Which of the following is the correct factorization of $$x^2 + 11x + 24$?

Accepted Answer

$$(x + 6)(x + 4)$$

Question 2

A trinomial $$x^2 + bx + c$ is said to be prime over the set of integers if:

Accepted Answer

It cannot be factored into a product of two binomials with integer coefficients.

Question 3

What is the correct factorization of $$x^2 + 5x + 6$?

Accepted Answer

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

Question 4

Which pair of integers multiplies to 24 and adds to 11, as required to factor $$x^2 + 11x + 24$?

Accepted Answer

6 and 4

Question 5

If a trinomial $$x^2 + bx + c$ has b = -7$ and c = 12$, what is its correct factorization?

Accepted Answer

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

Question 6

A medical researcher models the spread of a virus with the equation $$x^2 - 5x + 6 = 0$. What are the possible values for x$ (days) when the number of cases reaches zero?

Accepted Answer

2 and 3

Question 7

Which of the following trinomials is prime over the set of integers?

Accepted Answer

$$x^2 + 7x + 13$

Question 8

A chemical reaction is modeled by $$x^2 - x - 6$. What is the correct factorization to find the time when the reaction completes?

Accepted Answer

$$(x - 3)(x + 2)$$

Question 9

Which of the following is the correct factorization of $$x^2 + 9x + 8$?

Accepted Answer

$$(x + 8)(x + 1)$$

Question 10

A trinomial $$x^2 + bx + c$ has b = 6$ and c = 8$. What is its correct factorization?

Accepted Answer

$$(x + 4)(x + 2)$$

Question 11

If a trinomial $$x^2 + bx + c$ cannot be factored using integers, which of the following statements is true?

Accepted Answer

The trinomial is prime over the set of integers.

Question 12

A student tries to factor $$x^2 + 7x + 12$ and lists the pairs (1,12), (2,6), (3,4). Which pair should they use to factor the trinomial?

Accepted Answer

3 and 4

Question 13

Which of the following is the correct factorization of $$x^2 - 8x + 15$?

Accepted Answer

$$(x - 5)(x - 3)$$

Question 14

A trinomial $$x^2 + bx + c$ has b = -5$ and c = 6$. What is its correct factorization?

Accepted Answer

$$(x - 2)(x - 3)$$

Question 15

Which of the following is the correct factorization of $$x^2 + 7x + 6$?

Accepted Answer

$$(x + 6)(x + 1)$$

Question 16

A trinomial $$x^2 + bx + c$ has b = 5$ and c = 6$. Which of the following is the correct factorization?

Accepted Answer

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

Question 17

A trinomial $$x^2 + bx + c$ has b = -9$ and c = 20$. What is its correct factorization?

Accepted Answer

$$(x - 5)(x - 4)$$

Question 18

Which of the following is the correct factorization of $$x^2 + 8x + 15$?

Accepted Answer

$$(x + 5)(x + 3)$$

Question 19

A trinomial $$x^2 + bx + c$ has b = -6$ and c = 9$. What is its correct factorization?

Accepted Answer

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

Question 20

A trinomial $$x^2 + bx + c$ has b = 4$ and c = 3$. What is its correct factorization?

Accepted Answer

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

Factoring Trinomials with Leading Coefficient 1

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