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Factoring Quadratic Trinomials

Factoring Quadratic Trinomials. Put in descending order of exponents like ax ² +bx+c and multiply a*c Find two numbers whose product is (a*c), BUT whose sum is ‘b’ Rewrite ax ² + [larger factor]x + [smaller factor]x +c ( larger factor takes the same sign as ‘b’)

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Factoring Quadratic Trinomials

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  1. Factoring Quadratic Trinomials

  2. Put in descending order of exponents like ax²+bx+c and multiply a*c • Find two numbers whose product is (a*c), BUT whose sum is ‘b’ • Rewrite ax²+ [larger factor]x + [smaller factor]x +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 OUTLINE

  3. Order and multiply a*c • Find factors of (a*c), but their sum is ‘b’ • Write the new polynomial • Double Factor • Factor the binomial • Write a pair ofbinomials • Factors of 8 Sum of 6? • 1,8 9 • 2,4 6 • -1,-8 -9 • -2,-4 -6 • x²+4x+2x+8 • x(x+4) +2(x+4) • x(x+4) +2(x+4) • (x+4)(x+2) Example 1Factor x²+6x+8

  4. Factors of –21,Sum of –4? • 1,-21 -20 • 3,-7 -4 • -1,21 20 • -3,7 4 • x² -7x+3x – 21 • x(x-7) +3(x-7) • x(x-7) +3(x-7) • (x-7) (x+3) • Order and multiply a*c • Find factors of (a*c), but their sum is ‘b’ • Rewrite the new polynomial • Double Factor • Factor the binomial • Write a pair of binomials Example 2Factor x²–4x -21

  5. Order and multiply a*c • Find factors of (a*c), but their sum is ‘b’ • Rewrite the new polynomial • Double Factor • Factor the binomial • Write a pair of binomials • Factors of 30Sum 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) Example 3Factor 2x² –13x +15

  6. Order and multiply a*c • Find factors of (a*c), but their sum is ‘b’ • Rewrite the new polynomial • Double Factor • Factor the binomial • Write a pair of binomials • Factors of -400Sum of 0? • 1, -400 -399 • 2, -200 -198 • 4, -100 -96 • 5, -80 -76 • 20, -20 0 • 16r² +20r -20r -25 • 4r(4r +5) - 5(4r +5) • 4r(4r +5) +5(4r +5) • (4r +5)(4r -5) Example 4Factor 16r² - 25

  7. Factor out the GCF first • Order and multiply a*c • Find factors of (a*c), but their sum is ‘b’ • Rewrite the new polynomial • Double Factor • Factor the binomial • Write a pair of binomials • 2y(y2 + 7y – 30) • Factor –30Sum 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(y+10) –3(y+10) • y(y+10) –3(y+10) • (y+10) (y-3) Example 5Factor 2y3+14y2-60y

  8. Factor the following • x² +2x –80 • 3y² -22y –16 • 4w2 – 81 • 2x4 +12x3 – 14x2 Check your understanding

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