Question 1

Which of the following is the correct factorization by grouping for the polynomial $$6x^2 - 2x + 4x - 3$?

Accepted Answer

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

Question 2

What is the greatest common factor (GCF) of the terms $$2x$$ and $$-3 in $$the polynomial $$6x^2 - 2x + 4x - 3$ when factoring by grouping?

Accepted Answer

$$1$$

Question 3

Given the trinomial $$x^2 + 7x + 12$, which of the following is its correct factorization?

Accepted Answer

$$(x+3)(x+4)$$

Question 4

Which pair of numbers multiplies to $$12$$ and adds to $$7 in $$the trinomial $$x^2 + 7x + 12$?

Accepted Answer

$$3$$ and $$4$$

Question 5

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

Accepted Answer

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

Question 6

If you are factoring $$x^2 + 11x + 24$, which pair of numbers should you use?

Accepted Answer

$$3$$ and $$8$$

Question 7

Which of the following is NOT a correct step in factoring by grouping?

Accepted Answer

Combine all terms into a single group before factoring

Question 8

What is the solution set for the equation $$3x(x^2 - 16) = 0$?

Accepted Answer

$$x = 0, x = 4, x = -4$$

Question 9

Which equation is in quadratic form and can be solved by substitution?

Accepted Answer

$$3x^2 + 7x + 2 = 0$

Question 10

If you factor $$x^2 + 7x + 12$ and set each factor equal to zero, what are the solutions to the equation?

Accepted Answer

$$x = -3, x = -4$$

Question 11

Which property is used when you multiply both sides of an equation by the same nonzero number?

Accepted Answer

Multiplication property of equality

Question 12

What is the first step in solving $$x^2 + 5x + 6 = 0$?

Accepted Answer

Factor the quadratic expression

Question 13

Which of the following is a solution to $$x^2 + 11x + 24 = 0$?

Accepted Answer

$$x = -3$$

Question 14

When factoring $$x^2 + bx + c$, what must the two numbers do?

Accepted Answer

Multiply to $$c$$ and add to $$b$$

Question 15

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

Accepted Answer

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

Question 16

If you solve $$x^2 + 8x + 15 = 0$ by factoring, what are the solutions?

Accepted Answer

$$x = -3, x = -5$$

Question 17

Which of the following is a real-world application of factoring trinomials?

Accepted Answer

Calculating the break-even points for a business profit equation

Question 18

If a quadratic equation models the height $$h (in $$meters) of a ball thrown upward as $$h = -4.9t^2$ + 20t + 1$$, what does factoring help you find?

Accepted Answer

The times when the ball hits the ground

Question 19

Which step is necessary before factoring by grouping in $$ax^2 + bx + cx + d$?

Accepted Answer

Group the terms into two pairs

Factoring Polynomials and Trinomials in College Algebra

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