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Factoring Quadratic Polynomials Practice Problems

By — McGraw-Hill Professional
Updated on Sep 26, 2011

Factoring Quadratic Polynomials Practice Problems

Set 1: Facoring Quadratic Polynomials in Two Steps - Step 1: Determine the Signs

To review factoring quadratic polynomials, go to Factoring Quadratic Polynomials Help

Practice

Determine whether to begin the factoring as ( x + __)( x + __), ( x – __)( x – __), or ( x – __)( x + __).

1. x 2 – 5 x – 6 =

2. x 2 + 2 x + 1 =

3. x 2 + 3 x – 10 =

4. x 2 – 6 x + 8 =

5. x 2 – 11 x – 12 =

6. x 2 – 9 x + 14 =

7. x 2 + 7 x + 10 =

8. x 2 + 4 x – 21 =

Solutions

1. x 2 – 5 x – 6 = ( x –__)( x + __)

2. x 2 + 2 x + 1 = ( x + __)( x + __)

3. x 2 + 3 x – 10 = ( x – __)( x + __)

4. x 2 – 6 x + 8 = ( x – __)( x – __)

5. x 2 – 11 x – 12 = ( x – __)( x + __)

6. x 2 – 9 x + 14 = ( x – __)( x – __)

7. x 2 + 7 x + 10 = ( x + __)( x + __)

8. x 2 + 4 x – 21 = ( x – __)( x + __)

Set 2: Factoring Quadratic Polynomials in Two Steps - Step 2: Determine the Constants

To review what factors to check, go to Factoring Quadratic Polynomials Help.

Practice

Factor the quadratic polynomial.

1. x 2 – 5 x – 6 =

2. x 2 + 2 x + 1 =

3. x 2 + 3 x – 10 =

4. x 2 – 6 x + 8 =

5. x 2 – 11 x – 12 =

6. x 2 – 9 x + 14 =

7. x 2 + 7 x + 10 =

8. x 2 + 4 x – 21 =

9. x 2 + 13 x + 36 =

10. x 2 + 5 x – 24 =

Solutions

1. x 2 – 5 x – 6 = ( x – 6)( x + 1)

2. x 2 + 2 x + 1 = ( x + 1)( x + 1) = ( x + 1) 2

3. x 2 + 3 x – 10 = ( x + 5)( x – 2)

4. x 2 – 6 x + 8 = ( x – 4)( x – 2)

5. x 2 – 11 x – 12 = ( x – 12)( x + 1)

6. x 2 – 9 x + 14 = ( x – 7)( x – 2)

7. x 2 + 7 x + 10 = ( x + 5)( x + 2)

8. x 2 + 4 x – 21 = ( x + 7)( x – 3)

9. x 2 + 13 x + 36 = ( x + 4)( x + 9)

10. x 2 + 5 x – 24 = ( x + 8)( x – 3)

Set 3: Factoring Shortcuts When x2is the First Term - Shortcut 1

To review the factoring shortcut when the first term is x 2, go to Factoring Quadratic Polynomials Help.

Practice

1. x 2 – 6 x + 9 =

2. x 2x – 12 =

3. x 2 + 9 x – 22 =

4. x 2 + x – 20 =

5. x 2 + 13 x + 36 =

6. x 2 – 19 x + 34 =

7. x 2 – 18 x + 17 =

8. x 2 + 24 x – 25 =

9. x 2 – 14 x + 48 =

10. x 2 + 16 x + 64 =

11. x 2 – 49 =

( Hint : x 2 – 49 = x 2 + 0 x – 49)

Solutions

1. x 2 – 6 x + 9 = ( x – 3)( x – 3) = ( x – 3) 2

2. x 2x – 12 = ( x – 4)( x + 3)

3. x 2 + 9 x – 22 = ( x + 11)( x – 2)

4. x 2 + x – 20 = ( x + 5)( x – 4)

5. x 2 + 13 x + 36 = ( x + 4)( x + 9)

6. x 2 – 19 x + 34 = ( x – 2)( x – 17)

7. x 2 – 18 x + 17 = ( x – 1)( x – 17)

8. x 2 + 24 x – 25 = ( x + 25)( x – 1)

9. x 2 – 14 x + 48 = ( x – 6)( x – 8)

10. x 2 + 16 x + 64 = ( x + 8)( x + 8) = ( x + 8) 2

11. x 2 – 49 = ( x – 7)( x + 7)

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