Factoring Quadratic Trinomials 5/6/01

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Factoring Quadratic Trinomials5/6/01

• Objective you will factor quadratic polynomials
  into a pair of binomials

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OUTLINE

• Put in descending order of exponents like
  ax²bxc and multiply ac
• Find two numbers whose product is (ac), BUT
  whose sum is b
• Rewrite ax² larger factorx smaller factorx
  c ( larger factor takes the same sign as
  b)
• Factor the first pair of terms and factor the
  second pair of terms(by dividing out the common
  factor for each pair and if the 3rd term is
  negative, then factor it out also)
• Factor out the common binomial factor
• Write as a pair of binomials

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Example 1Factor x²6x8

• Order and multiply ac
• Find factors of (ac), but their sum is b
• Write the new polynomial
• Double Factor
• Factor the binomial
• Write a pair of binomials

• Factors of 8 Sum of 6?
• 1,8 9
• 2,4 6
• -1,-8 -9
• -2,-4 -6
• x²4x2x8
• x(x4) 2(x4)
• x(x4) 2(x4)
• (x4)(x2)

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Example 2Factor x²4x -21

• Factors of 21,Sum of 4?
• 1,-21 -20
• 3,-7 -4
• -1,21 20
• -3,7 4
• x² -7x3x 21
• x(x-7) 3(x-7)
• x(x-7) 3(x-7)
• (x-7) (x3)

• Order and multiply ac
• Find factors of (ac), but their sum is b
• Rewrite the new polynomial
• Double Factor
• Factor the binomial
• Write a pair of binomials

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Example 3Factor y²7y-30

• Order and multiply ac
• Find factors of (ac), but their sum is b
• Rewrite the new polynomial
• Double Factor
• Factor the binomial
• Write a pair of binomials

• Factor 30 Sum of 7?
• 1,-30 -29
• 2,-15 -13
• 3,-10 -7
• 5,-6 -1
• -1,30 29
• -2,15 13
• -3, 10 7
• -5,6 1
• y² 10y 3y 30
• y(y10) 3(y10)
• y(y10) 3(y10)
• (y10) (y-3)

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Example 4Factor 2x² 13x 15

• Order and multiply ac
• Find factors of (ac), but their sum is b
• Rewrite the new polynomial
• Double Factor
• Factor the binomial
• Write a pair of binomials

• Factors of 30 Sum of 13?
• 1,30 31
• 2,15 17
• 3,10 13
• 5,6 11
• -1-,30 -31
• -2,-15 -17
• -3,- 10 -13
• -5,-6 -11
• 2x² -10x -3x 15
• 2x(x -5) -3(x -5)
• 2x(x -5) -3(x -5)
• (x -5)(2x 3)

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Example 5Factor 15r² 44r 21

• Order and multiply ac
• Find factors of (ac), but their sum is b
• Rewrite the new polynomial
• Double Factor
• Factor the binomial
• Write a pair of binomials

• Factors of 315 Sum of 44?
• 1, 315 316
• 3, 105 108
• 5, 63 68
• 7, 45 52
• 9, 35 44
• 15r² 35r 9r 21
• 5r(3r 7) 3(3r 7)
• 5r(3r 7) 3(3r 7)
• (3r 7)(5r 3)

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Check your understanding (click to check each
step)6) Factor x² 2x 80 7)Factor 3y² -22y
16

• x² 2x 80 (no peeking)
• Factors of 80 Sum of 2?
• -1, 80 79
• -2, 40 38
• -4, 20 16
• -8, 10 2
• x² 10x 8x 80
• x(x 10) 8(x 10)
• x(x 10) 8(x 10)
• (x 10)(x 8)

• 3y² -22y 16
• Factors of-48 Sum of 22
• 1, -48 -47
• 2, -24 -22
• 3y² -24y 2y 16
• 3y(y 8) 2(y 8)
• 3y(y 8) 2(y 8)
• (y -8)(3y 2)
• Now practice !!!