Algebra 1 Factoring Polynomials Test with Point Values (PDF)

Algebra 1 math test: Factoring Polynomials – Maths PDF

This factoring test for Algebra 1 covers factoring polynomials (Common Core A-SSE.A.2, A-SSE.B.3a, A-APR.B.3), with a free PDF to print.

Factoring test (Algebra 1) – first page of the printable PDF
This test checks factoring polynomials for Common Core A-SSE.A.2, A-SSE.B.3a, and A-APR.B.3. It has 9 questions worth 20 points in all, and you have 45 minutes. Write clear steps, because points are awarded for method as well as for the final answer. Leave a few minutes to review.

Time and points

About this test
  • Grade: Algebra 1
  • Chapter: Factoring Polynomials
  • Standards: A-SSE.A.2, A-SSE.B.3a, A-APR.B.3
  • Time: 45 minutes
  • Total: 20 points

Factoring test: questions

Question 1 – Greatest common factor [2 pts]

Factor \(24x^{3} + 16x^{2}\).

Question 2 – Simple trinomial [2 pts]

x?xx²?24
Area model for question 2.

Factor \(x^{2} + 11x + 24\).

Question 3 – Mixed signs [2 pts]

Factor \(x^{2} – 4x – 32\).

Question 4 – Leading coefficient 3 [2 pts]

Factor \(3x^{2} + 7x – 6\).

Question 5 – Difference of squares [2 pts]

Factor \(x^{2} – 81\).

Question 6 – Perfect square trinomial [2 pts]

Factor \(x^{2} – 14x + 49\).

Question 7 – Factor completely and find zeros [3 pts]

Consider \(3x^{2} – 48\).

  1. Factor completely. (2 points)
  2. Find the values of \(x\) that make the expression 0. (1 point)

Question 8 – Rectangle dimensions [3 pts]

?x + 2x² + 10x + 16
Area \(x^{2} + 10x + 16\).

A rectangle has area \(x^{2} + 10x + 16\) square meters and width \(x + 2\) meters.

  1. Factor the area. (2 points)
  2. Find the length. (1 point)

Question 9 – Ball landing time [2 pts]

xy1234-1010203040(0, 0)(3, 0)
Height of a ball in feet.

A ball’s height in feet is \(h(t) = -16t^{2} + 48t\). Factor the expression and find when the ball lands.

View solution

Key facts behind this factoring test

Key facts
  • Factor out the greatest common factor (GCF) first.
  • For x² + bx + c, find two numbers with product c and sum b.
  • Difference of squares: a² – b² = (a + b)(a – b).
  • Perfect square trinomials: a² ± 2ab + b² = (a ± b)².
  • If a product is zero, one of its factors is zero, so factored form shows the zeros.

How to use this factoring test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

Prepare for the test

All Algebra 1 chapters: Algebra 1 math.

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