Algebra 1 Factoring Polynomials Worksheet (PDF)

Algebra 1 math worksheet: Factoring Polynomials – Maths PDF

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This factoring practice worksheet 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 practice worksheet (Algebra 1) – first page of the printable PDF

Use these 20 problems to master factoring polynomials (Common Core A-SSE.A.2, A-SSE.B.3a, and A-APR.B.3). You will factor out the GCF, factor trinomials and special patterns, and use factored form to find zeros and solve area and projectile problems. They move from quick warm-ups to multistep word problems, so slow down on the last six and check that each answer makes sense.

Algebra 1 · Common Core State Standards: A-SSE.A.2, A-SSE.B.3a, A-APR.B.3

Factoring practice worksheet: exercises 1 to 10

Exercise 1 – Greatest common factor

Find the GCF of 12 and 18, and the GCF of \(8x^{2}\) and \(12x\).

Exercise 2 – Factor out the GCF

GCF steps.

Factor \(12x + 18\).

Exercise 3 – GCF with powers

Factor \(15x^{3} – 10x^{2}\).

Exercise 4 – Trinomial with positive terms

Find the missing sides.

Factor \(x^{2} + 7x + 12\).

Exercise 5 – Another positive trinomial

Factor \(x^{2} + 10x + 21\).

Exercise 6 – Negative constant

Factor \(x^{2} – x – 12\).

Exercise 7 – Negative middle term

Factor \(x^{2} – 8x + 15\).

Exercise 8 – Mixed signs

Factor \(x^{2} + 4x – 21\).

Exercise 9 – Trinomial with a equal to 3

Factor \(3x^{2} + 11x + 6\).

Exercise 10 – Trinomial with a equal to 2

Factor \(2x^{2} – 9x + 10\).

Exercises 11 and up

Exercise 11 – Harder trinomial

Factor \(6x^{2} + x – 2\).

Exercise 12 – Difference of squares

The picture of \(a^{2} – b^{2}\).

Factor \(x^{2} – 49\).

Exercise 13 – Difference of squares with a coefficient

Factor \(4x^{2} – 25\).

Exercise 14 – Perfect square trinomials

Perfect square patterns.

Factor \(x^{2} + 10x + 25\) and \(9x^{2} – 12x + 4\).

Exercise 15 – Factor completely

Factor \(2x^{2} – 18\) completely.

Exercise 16 – Rectangle dimensions

A rectangle with area \(x^{2} + 9x + 14\).

A rectangle has area \(x^{2} + 9x + 14\) square feet. Factor to find possible expressions for its length and width.

Exercise 17 – Ball in the air

Height of a ball in feet.

A ball’s height in feet is \(h(t) = -16t^{2} + 64t\). Factor the expression and find when the ball is on the ground.

Exercise 18 – Zeros of a function

Graph of the function.

Find the zeros of \(f(x) = x^{2} – 5x – 14\) by factoring.

Exercise 19 – Garden dimensions

A rectangular garden has area \(3x^{2} + 12x\) square yards and width \(3x\) yards. Factor the area to find the length.

Exercise 20 – Check by substitution

Show that \(x^{2} – 16\) and \((x – 4)(x + 4)\) have the same value when \(x = 9\).

Exercise 21 – Mental math

Use a difference of squares to compute \(51^{2} – 49^{2}\) without a calculator.

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Key facts behind this factoring practice worksheet

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 practice worksheet

Work through the exercises in order: they go from simple to challenging. Write every step on paper, then compare with the solutions page and redo any exercise you missed the next day.

Algebra 1 Factoring Polynomials Worksheet (PDF)

Factoring practice worksheet: exercises 1 to 10

Exercises 11 and up

Key facts behind this factoring practice worksheet

How to use this factoring practice worksheet

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