Factoring Polynomials

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Presentation transcript:

Factoring Polynomials

Multiplying Polynomials (x-5)(2x+1) (y2 + 3y +6)(y-4)

Multiplying Polynomials (x2 + 2) (x-8) (y3-4)(y2 +3y-6)

Checklist Greatest Common Factor Leading coefficient a=1 ax2 +bx+c

Factoring 4x-20 =4(x-5) -3x2 +12x+27 =-3x(x-4x-9) =3x(-x+4x-9) 2(x-y)-a(x-y) =(x-y)(2-a)

Factor 4x-48 63x3 + 7x2 +21x 2(x-y)-a(x-y) x2 (x–5) + 4(5 –x)

Factor b2 + 8b + 7 Diamond Way: Multiply 7 1 7 8 Add (x ) (x ) +1 +7

Factor using the Diamond Check your Work X2 + 4x -12 n2− n − 56 5v2− 30v + 40 (x2-81)

Factor Using the Diamond Check your Work n2+ 6n + 8 2x2+ 6n − 108 (x2-144) x2 /3-x- 10/3

Activity Challenge the other groups Create 3 problems to factor Rules: Needs to be a trinomial Highest exponent is a 2 Can have a leading coefficient a=1 **Make sure you check your work**

Warm Up Use the Diamond Method 4x2 + 8x – 60

Warm Up Use the Diamond Method 1/2x2+x-15/2

Checklist Greatest Common Factor Leading coefficient a=1 ax2 +bx+c

Guess and Check 3x2-2x-5 ( x )( x )

Practice Check your work 5n2 -18n + 9 −6a2 − 25a − 25 16b2 + 60b − 100

Practice 5n2 -18n + 9 −6a2 − 25a − 25 16b2 + 60b − 100 1/3x2 +2/3x-8 Check your work 5n2 -18n + 9 −6a2 − 25a − 25 16b2 + 60b − 100 1/3x2 +2/3x-8

Box Method (only works if common factors have been removed) 2x2 + x − 6 Step 1: Multiply the leading coefficient and the constant 2(6) =12 Step 2: Find the common factors: Of 12 2x2 4x -3x -6

2x2 + x − 6 2x 2x2 4x -3x -6 -3 -2 x (2x-3)(x-2)

Factor Use the box method 3x2 – 7x –6 5x2+ 19n + 12 7x2+ 53a + 28

Factor by Grouping 2 9 2n2+ 3n − 9 Step 1: Multiply the leading coefficient with the constant 2(-9) =-18 Step 2: Find the factors of 18 that add to 3 2 9

2n2+ 3n − 9 Step 3: 2n2+6n-3n − 9 Step 4: Split the polynomial down the middle (2n2+ 6n)+(3n − 9) Step 5: Greatest Common Factor 2n(n+3) + -3(n+3)

2n2+ 3n − 9 2n(n+3) + -3(n+3) Step 6: Common Factor (n+3)(2n-3)

Practice 5n2 +19+12 -12f2 -38f+22 8x3 – 64x2 +x-8 12x2 u+3x2 v+28yu+7yv

Step 1) Multiply leading coefficient and constant Factor 3x2 − 2x − 5 Slide and Divide: Step 1) Multiply leading coefficient and constant 3 x2 − 2x − 5 -15

x2 − 2x − 15 Step 2) Use the Diamond Method (x ) (x ) -5 +3 -15 -5 3 Multiply -15 -5 3 -2 Add (x ) (x ) -5 +3

. (x-5)(x+3) Step 3) Divide (x- ) (x+ ) Step 4) Simplify (x- ) (x+3) Step 5) Multiply (3x-5)(x+3) ─

Factor 2v2 + 11v + 5 3m2 – 10m + 8 15 m3 +24m2 +9m 2y^2(4x^2+9)