Solving Quadratic Equations by Factoring - Quick Review and Helpful Hints

Sep 14, 2026

Uploaded by Ben

Solving quadratic equations by factoring focuses on converting a quadratic to factored form and applying the zero-product property. The materials guide students to set the product equal to 0, then solve by setting each factor equal to 0 to find the solution values. Worked examples and word problems connect factoring to roots, x-intercepts, and model-based zeros from area and projectile-height contexts. Answer keys provide step-by-step reasoning for multiple practice items.

LanguageEnglish

CategoryExam

FormatPDF

Pages3

Reading Time8 min

AccessFree to download

Quick Review and Helpful Hints

Zero-product property

Roots and x-intercepts

Word Problems

Answer Keys - Step-by-Step Explanations

Practice 􀀏 Progress 􀀏 Succeed | GED Math ~~ ~~ [E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com) Solving Quadratic Equations by Factoring | Name: | D | ate: | S | core: / 18 | | --- | --- | --- | --- | --- | Quick Review and Helpful Hints Set the equation equal to 0, factor the quadratic, then use the zero-product property: if a product is 0, at least one factor is 0. So if (x 􀀀 p)(x 􀀀 q) = 0, then x = p or x = q. ▷ Example: Solve x2 + 5x + 6 = 0 . Work: Factor: (x + 2)(x + 3) = 0 . Set each factor to 0: x + 2 = 0 or x + 3 = 0 . ⋆ Answer: x = 􀀀2 or x = 􀀀3 Roots: where the curve meets the x-axis. ♦ Word Problems 15. A square sign has area 4 square feet. If side length is represented by x, solve x2 􀀀 4 = 0 for the possible mathematical values of x. 16. A projectile-height model has zeros found by solving x2 + 9x + 20 = 0 . Solve for the two zero values. 17. A rectangular area model becomes zero at the boundary values of x2 􀀀 6x + 8 = 0 . Solve for those values. 18. If (x 􀀀 3)(x + 5) = 0, 􀀂nd all values of x. [E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com) 1 Scan Me Practice 􀀏 Progress 􀀏 Succeed | GED Math ~~ ~~ [E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com) Answer Keys Step-by-Step Explanations 1. Start by naming the process: Factor the quadratic, then use the zeroproduct property by setting each factor equal to zero. The setup/work is (x + 2)(x + 3) = 0, so x = 􀀀2 or 􀀀3 . So the 􀀂nal answer is x = 􀀀2, 􀀀3 . 2. A good way to think about this is: Factor the quadratic, then use the zeroproduct property by setting each factor equal to zero. The setup/work is (x 􀀀 3)(x 􀀀 4) = 0, so x = 3 or 4. So the 􀀂nal answer is x = 3 , 4. 3. Step by step: Factor the quadratic, then use the zero-product property by setting each factor equal to zero. The setup/work is (x + 3)(x 􀀀 2) = 0, sox = 2 or 􀀀3 . So the 􀀂nal answer is x = 2 , 􀀀3 . 4. Take it one move at a time: Factor the quadratic, then use the zero-product property by setting each factor equal to zero. The setup/work is (x􀀀3)(x+3) = 0, so x = 3 or 􀀀3 . So the 􀀂nal answer is x = 3 , 􀀀3 . 5. Start by naming the process: Factor the quadratic, then use the zero-product property by setting each factor equal to zero. The setup/work is x(x 􀀀 5) = 0 , so x = 0 or 5. So the 􀀂nal answer is x = 0 , 5. 6. A good way to think about this is: Factor the quadratic, then use the zeroproduct property by setting each factor equal to zero. The setup/work is (x + 4)(x 􀀀 2) = 0, so x = 2 or 􀀀4 . So the 􀀂nal answer is x = 2 , 􀀀4 . 7. Step by step: Factor the quadratic, then use the zero-product property by setting each factor equal to zero. The setup/work is (x 􀀀 2)2 = 0, so x = 2 (one repeated root) . So the 􀀂nal answer is x = 2 . 8. Take it one move at a time: Factor the quadratic, then use the zero-product property by setting each factor equal to zero. The setup/work is

FAQs

What is the main method for solving quadratic equations by factoring?

Factor the quadratic, set the factored expression equal to 0, and use the zero-product property. Then solve by setting each factor equal to 0.

How does the zero-product property help when you factor a quadratic?

If (x − p)(x − q) = 0, then at least one factor must be 0. Solving each factor equal to 0 gives the possible values of x.

How are roots related to graphing in these problems?

Roots are where the curve meets the x-axis. For factored forms, the roots correspond to the x-values that make the quadratic equal to zero.

Sep 14, 2026

Uploaded by Ben