Algebra 1 Factoring Quiz with Answers – Free PDF

Contents

This algebra 1 factoring quiz asks 10 multiple-choice questions on factoring polynomials, and each answer comes with a short explanation.

Answer these 10 multiple-choice questions on factoring: GCF, trinomials, the special patterns, grouping and zeros of quadratics. Each has one correct answer, and each explanation points out a typical mistake.

Algebra 1Common Core: A-SSE.A.2 · A-SSE.B.3a

🎯 Factoring Polynomials – Algebra 1 math quiz

Score: 0 / 10

Answered: 0 / 10

Question 1

What is the greatest common factor of \(24x^{3}\) and \(36x^{2}\)?

A \(6x^{2}\)

B \(12x^{2}\)

C \(12x^{3}\)

D \(72x^{3}\)

Question 2

Factor \(6x^{2}-9x\) completely.

A \(3(2x^{2}-3x)\)

B \(3x(2x+3)\)

C \(3x(2x-3)\)

D \(x(6x-9)\)

Question 3

Factor \(x^{2}+9x+20\).

Area model.

A \((x+4)(x+5)\)

B \((x+2)(x+10)\)

C \((x+4)(x-5)\)

D \((x-4)(x-5)\)

Question 4

Factor \(x^{2}-2x-24\).

A \((x+6)(x-4)\)

B \((x-6)(x+4)\)

C \((x-8)(x+3)\)

D \((x-6)(x-4)\)

Question 5

Factor \(25x^{2}-49\).

A \((5x-7)^{2}\)

B \((5x+7)^{2}\)

C \((25x-7)(x+7)\)

D \((5x-7)(5x+7)\)

Question 6

Factor \(4x^{2}+12x+9\).

A \((4x+3)^{2}\)

B \((2x+3)(2x-3)\)

C \((2x+3)^{2}\)

D \((4x+3)(x+3)\)

Question 7

Factor \(2x^{2}+5x-3\).

A \((2x+1)(x-3)\)

B \((2x-3)(x+1)\)

C \((2x+3)(x-1)\)

D \((2x-1)(x+3)\)

Question 8

The graph shows \(y=x^{2}-x-12\). What are the solutions of \(x^{2}-x-12=0\)?

Graph of the parabola.

A \(x=4\) and \(x=3\)

B \(x=4\) and \(x=-3\)

C \(x=-4\) and \(x=3\)

D \(x=12\) and \(x=-1\)

Question 9

Factor \(x^{3}+3x^{2}+4x+12\) by grouping.

A \((x^{2}+4)(x+3)\)

B \((x^{2}+3)(x+4)\)

C \((x^{2}+4)(x-3)\)

D \((x^{2}-4)(x+3)\)

Question 10

A rectangle has area \(x^{2}+8x+12\) and width \(x+2\). What is its length?

Rectangle.

A \(x+4\)

B \(x+10\)

C \(x+6\)

D \(x+14\)

🎉 Quiz complete!

0 / 10

How does this quiz work?

Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.

What should you review before the quiz?

Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.

Remember:

Always factor out the greatest common factor first.
For x² + bx + c, find two numbers with product c and sum b.
For ax² + bx + c, split the middle term using two numbers with product ac, then factor by grouping.
Patterns: a² − b² = (a + b)(a − b) and a² ± 2ab + b² = (a ± b)².
The zero product property turns a factored equation into its zeros, the x-intercepts of the graph.