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Factoring Quadratic Trinomials 5/6/01. Objective: you will factor quadratic polynomials into a pair of binomials. OUTLINE. 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’

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Factoring quadratic trinomials 5 6 01

Factoring Quadratic Trinomials5/6/01

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


Outline
OUTLINE

  • 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


Example 1 factor x 6x 8

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 of binomials

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


Example 2 factor x 4x 21

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)

Example 2Factor x²–4x -21

  • 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 3 factor y 7y 30

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

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 3Factor y²+7y-30


Example 4 factor 2x 13x 15

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 4Factor 2x² –13x +15


Example 5 factor 15r 44r 21

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 315Sum 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)

Example 5Factor 15r² +44r +21


Check your understanding click to check each step 6 factor x 2x 80 7 factor 3y 22y 16

+2x –80 (no peeking)

Factors of –80Sum 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-48Sum 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 !!!

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


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