Factoring Practice Problems

Factoring Practice Problems

Set 1: Factoring Using the Distributive Property

To review factoring, go to Factoring Help

Practice

1. 4x – 10y =
2. 3x + 6y – 12 =
3. 5x ² + 15 =
4. 4x ² + 4x =
5. 4x ³ – 6x ² + 12x =
6. –24xy ² + 6x ² + 18x =
7. 30x ⁴ – 6x ² =
8. 15x ³y ²z ⁷ – 30 xy ²z ⁴ + 6x ⁴y ²z ⁶ =

Solutions

Set 2: Factoring Negative Quantities

To review factoring a negative quantity, go to Factoring Help.

Practice

Factor a negative quantity from the expression.

1. 28 xy ² – 14 x =
2. 4 x + 16 xy =
3. –18 y ² + 6 xy =
4. 25 + 15 y =
5. –8 x ² y ² – 4 xy ² =
6. –18 x ² y ² – 24 xy ³ =
7. 20 xyz ² – 5 yz =

Solutions

Set 3: Factoring Using the Associative Property

To review the associative and distributive properties, go to Factoring Help.

Practice

1. 2 (x – y) + 3y (x – y) =
2. 4 (2 + 7x) – x (2 + 7x) =
3. 3 (3 + x)+ x (3 + x) =
4. 6x (4 – 3x) – 2y (4 – 3x) – 5 (4 – 3x) =
5. 2x + 1 + 9x (2x + 1) =
6. 3 (x – 2y) ⁴ + 2x (x – 2y) ⁴ =

Solutions

Set 4: More Factoring

To review factoring an algebraic expression raised to different powers, go to Factoring Help.

Practice

1.  8( x + 2) ³ + 5( x + 2) ² =
2. –4( x + 16) ⁴ + 9( x + 16) ² + x + 16 =
3. ( x + 2 y ) ³ – 4( x + 2 y ) =
4. 2( x ² – 6) ⁹ +( x ² – 6) ⁴ + 4( x ² – 6) ³ +( x ² – 6) ² =
5. (15 xy – 1)(2 x – 1) ³ – 8(2 x – 1) ² =