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Factoring Practice Problems

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

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

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

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

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

Set 3: Factoring Using the Associative Property

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

Practice

  1. 2 (xy) + 3y (xy) =
  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

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

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 =
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