dividing polynomials
DESCRIPTION
Dividing Polynomials. Synthetic Division Used to factor polynomials and find the roots / zeros. Synthetic Division. Same idea as synthetic substitution. Remember to use 0 as the coefficient of any missing terms!. Synthetic Division. Divide f(x) = x 3 – x + 1 by x + 2. - PowerPoint PPT PresentationTRANSCRIPT
Dividing Polynomials
Synthetic Division
Used to factor polynomials and find the roots / zeros.
Synthetic Division
Same idea as synthetic substitution.
Remember to use 0 as the coefficient of any missing terms!
Synthetic Division
Same idea as synthetic substitution.
Remember to use 0 as the coefficient of any missing terms!
Divide f(x) = x3 – x + 1 by x + 2.
Synthetic Division
Same idea as synthetic substitution.
Remember to use 0 as the coefficient of any missing terms!
Divide f(x) = x3 – x + 1 by x + 2.
-2 1 0 -1 1
Synthetic Division
Same idea as synthetic substitution.
Remember to use 0 as the coefficient of any missing terms!
Divide f(x) = x3 – x + 1 by x + 2.
-2 1 0 -1 1
1
Synthetic Division
Same idea as synthetic substitution.
Remember to use 0 as the coefficient of any missing terms!
Divide f(x) = x3 – x + 1 by x + 2.
-2 1 0 -1 1
-2
1
Synthetic Division
Same idea as synthetic substitution.
Remember to use 0 as the coefficient of any missing terms!
Divide f(x) = x3 – x + 1 by x + 2.
-2 1 0 -1 1
-2
1 -2
Synthetic Division
Same idea as synthetic substitution.
Remember to use 0 as the coefficient of any missing terms!
Divide f(x) = x3 – x + 1 by x + 2.
-2 1 0 -1 1
-2 4
1 -2
Synthetic Division
Same idea as synthetic substitution.
Remember to use 0 as the coefficient of any missing terms!
Divide f(x) = x3 – x + 1 by x + 2.
-2 1 0 -1 1
-2 4
1 -2 3
Synthetic Division
Same idea as synthetic substitution.
Remember to use 0 as the coefficient of any missing terms!
Divide f(x) = x3 – x + 1 by x + 2.
-2 1 0 -1 1
-2 4 -6
1 -2 3
Synthetic Division
Same idea as synthetic substitution.
Remember to use 0 as the coefficient of any missing terms!
Divide f(x) = x3 – x + 1 by x + 2.
-2 1 0 -1 1
-2 4 -6
1 -2 3 -5
Synthetic Division
Same idea as synthetic substitution.
Remember to use 0 as the coefficient of any missing terms!
Divide f(x) = x3 – x + 1 by x + 2.
-2 1 0 -1 1
-2 4 -6
1 -2 3 -5
x2 x constant
remainder
Synthetic Division
Same idea as synthetic substitution.
Remember to use 0 as the coefficient of any missing terms!
Divide f(x) = x3 – x + 1 by x + 2.
-2 1 0 -1 1
-2 4 -6
1 -2 3 -5
2x
532xx2
x2 x constant
remainder
Factoring
Use one factor to divide the polynomial and find the rest.
Factoring
Use one factor to divide the polynomial and find the rest.Completely factor f(x) = x3 – 10x2 + 19x + 30 given that f(6) = 0.
Factoring
Use one factor to divide the polynomial and find the rest.
First, divide f(x) = x3 – 10x2 + 19x + 30 by x – 6.
Completely factor f(x) = x3 – 10x2 + 19x + 30 given that f(6) = 0.
Factoring
Use one factor to divide the polynomial and find the rest.
First, divide f(x) = x3 – 10x2 + 19x + 30 by x – 6.
6 1 -10 19 30
6 -24 -30
1 -4 -5 0
Completely factor f(x) = x3 – 10x2 + 19x + 30 given that f(6) = 0.
Factoring
Use one factor to divide the polynomial and find the rest.
First, divide f(x) = x3 – 10x2 + 19x + 30 by x – 6.
6 1 -10 19 30
6 -24 -30
1 -4 -5 0x2 – 4x – 5
Completely factor f(x) = x3 – 10x2 + 19x + 30 given that f(6) = 0.
Factoring
Use one factor to divide the polynomial and find the rest.
First, divide f(x) = x3 – 10x2 + 19x + 30 by x – 6.
6 1 -10 19 30
6 -24 -30
1 -4 -5 0x2 – 4x – 5
Completely factor f(x) = x3 – 10x2 + 19x + 30 given that f(6) = 0.
Second, factor the binomial x2 – 4x – 5.
Factoring
Use one factor to divide the polynomial and find the rest.
First, divide f(x) = x3 – 10x2 + 19x + 30 by x – 6.
6 1 -10 19 30
6 -24 -30
1 -4 -5 0x2 – 4x – 5
Completely factor f(x) = x3 – 10x2 + 19x + 30 given that f(6) = 0.
Second, factor the binomial x2 – 4x – 5.
x2 – 4x – 5 = (x – 5)(x + 1)
Factoring
Use one factor to divide the polynomial and find the rest.
First, divide f(x) = x3 – 10x2 + 19x + 30 by x – 6.
6 1 -10 19 30
6 -24 -30
1 -4 -5 0x2 – 4x – 5
Completely factor f(x) = x3 – 10x2 + 19x + 30 given that f(6) = 0.
Second, factor the binomial x2 – 4x – 5.
x2 – 4x – 5 = (x – 5)(x + 1)
So f(x) = (x – 6)(x – 5)(x + 1).
Practice
Use synthetic division to completely factor
f(x) = x3 – 10x2 + 8x + 64 given that f(-2) = 0.