Factoring Trinomials

1
Factoring Trinomials

• Pull out the GCF.
• Multiply ac.
• List all factors of ac.
• Find the factors of ac that add up to b.
• Replace b with those factors so that there are
  now four terms.
• Factor by grouping.
• Check if you can factor any further.

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Example 1 7x228x28

• 7x228x28 GCF7
• 7(x24x4)

• 7(1x24x4) Multiply a and c.
• a1 c4, ac 4

• List factors of 4.
• (1, 4) (-1, -4) (2, 2) (-2, -2)

• Pick factors that add to b. 7(1x24x4)
• (1, 4) (-1, -4) (2, 2) (-2, -2) 22 4

3

• Substitute for b.
• 7(x24x4) 7(x22x2x4)

• Finish problem by factoring by grouping
• 7(x22x2x4)
• 7x(x2)2(x2)
• 7x(x2)2(x2)
• 7(x2)(x2)

• Can you factor any further?
• No, the variables in the parentheses dont have
  exponents.

4
Example 2 x6 - 6x4 - 16x2

• x6 6x4 16x2 GCFx2
• x2(x4 6x2 16)

• x2(1x4 6x - 16) Multiply a and c.
• a1 c -16, ac -16

5

• List factors of 16.
• (1, -16)
• (-1, 16)
• (2, -8)
• (-2, 8)
• (4, -4)

• Find the sum that adds to b.
• (1, -16) -15
• (-1, 16) 15
• (2, -8) -6
• (-2, 8) 6
• (4, -4) 0

• (2, -8) -6

6

• Substitute for b.
• x2(x4 - 6x2 - 16) x2(x4 - 8x2 2x2 - 16)
• OR x2(x4 - 6x2 - 16) x2(x4 2x2 - 8x2 - 16)

• Finish problem by factoring by grouping
• x2(x4 8x2 2x2 -16)
• x2x2(x2- 8) 2(x2 - 8)
• x2x2(x2 - 8) 2(x2 - 8)
• x2(x2 - 8)(x2 2)

• Check to see if we can factor further.
• We have exponents inside parentheses, but no
  perfect squares and no trinomials.

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Example 3 x2 2/3xy 1/9y2

• x2 2/3xy 1/9y2 GCF1
• x2 2/3xy 1/9y2

• (1x2 2/3xy 1/9y2) Multiply a and c.
• a1 c 1/9, ac 1/9

• List factors of 1/9.
• (1, 1/9) (-1, -1/9) (-1/3, -1/3) (1/3, 1/3)

8

• Pick factors that add to b x2 2/3xy 1/9y2
• (1, 1/9) 10/9
• (-1, -1/9) -10/9
• (-1/3, -1/3) -2/3
• (1/3, 1/3) 2/3

• Substitute for b.
• x2 2/3xy 1/9y2
• x2 1/3xy 1/3xy 1/9y2

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• Finish problem by factoring by grouping
• x2 1/3xy 1/3xy 1/9y2
• x(x 1/3y) 1/3y(x - 1/3y)
• x(x 1/3y) 1/3y(x - 1/3y)
• (x-1/3y)(x-1/3y)

• Can you factor any further?
• No, the variables in the parentheses dont have
  exponents.