Factor Quadratics Worksheets (a = 1)

There are four sets of factoring quadratics worksheets:

• Factoring Quadratics (a = 1)
  
• Factoring Quadratics (a > 1)
  
• Factor Difference of Squares
  
• Factor Perfect Square Quadratics
  

Examples, solutions, videos, and worksheets to help Grade 7 and Grade 8 students learn how to factor quadratics, ax² + bx + c for a = 1.

How to factor quadratics?

There are five sets of factoring quadratics worksheets (a = 1).

• Factor Quadratics (b>0, c>0).
• Factor Quadratics (b>0, c<0).
• Factor Quadratics (b<0, c>0).
• Factor Quadratics (b<0, c<0).
• Factor Quadratics (b & c can be positive or negative).

These are the steps to factor quadratics:

1. Make sure the quadratic is written in standard form, which is in the form of ax² + bx + c, where a, b, and c are constants.
2. Look for any common factors among the coefficients (a, b, and c) and factor them out. This step is important to simplify the quadratic before further factoring.
3. Identify two numbers that multiply to give the constant term (c) and add up to give the coefficient of the middle term (b).
4. Rewrite the middle term (bx) using the two numbers found in the previous step.
5. Group the terms of the quadratic by grouping the first two terms and the last two terms.
6. Factor out the greatest common factor (GCF) from each group, if possible.
7. Apply the distributive property to factor out the common binomial factor.

Example: Factor the quadratics: x² - 6x + 5.

1. The quadratics is already in standard form.
2. There are no common factors among the coefficients.
3. The numbers that multiply to give 5 and add up to give -6 are -5 and -1.
4. Rewrite the middle term:
   x² - 5x - x + 5
5. Group the terms:
   (x² - 5x) + (-x + 5)
6. Factor out the GCF from each group:
   x(x - 5) - 1(x - 5)
7. Apply the distributive property:
   (x - 1)(x - 5)

Therefore, the factored form of the quadratics x² - 6x + 5 is (x - 1)(x - 5).

Have a look at this video if you need to review how to factor quadratics.

• Factor Quadratics

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Scroll down the page for more Factor Quadratics Worksheets.

 

More Factor Quadratics Worksheets

Printable
(Answers on the second page.)
Factor Quadratics Worksheet #1 (b>0, c>0)
Factor Quadratics Worksheet #2 (b>0, c<0)
Factor Quadratics Worksheet #3 (b<0, c>0)
Factor Quadratics Worksheet #4 (b<0, c<0)
Factor Quadratics Worksheet #5 (b & c can be positive or negative)

Online or Generated
Factor Binomials by Difference of Squares
Factor Perfect Square Trinomials

Factor Trinomials or Quadratic Equations
Factor Different Types of Trinomials 1
Factor Different Types of Trinomials 2

Solve Trinomials using Quadratic Formula
Find Discriminants of Quadratic Polynomials

Related Lessons & Worksheets

Factor Quadratics (a > 1)
Factor Quadratics (common factors)

More Printable Worksheets

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