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 x^{2}is 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 ^{2} – x – 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 ^{2} – x – 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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