More Related Content Similar to Synthetic Division (20) More from Jimbo Lamb (20) Synthetic Division1. Extra Section
Synthetic Division
Fo r us e w it h li nea r fact ors 2. Warm-up
Divide.
(3x + 2x − x + 3) ÷ (x − 3)
3 2 3. Warm-up
Divide.
(3x + 2x − x + 3) ÷ (x − 3)
3 2
x − 3 3x + 2x − x + 3
3 2 4. Warm-up
Divide.
(3x + 2x − x + 3) ÷ (x − 3)
3 2
2
3x
x − 3 3x + 2x − x + 3
3 2 5. Warm-up
Divide.
(3x + 2x − x + 3) ÷ (x − 3)
3 2
2
3x
x − 3 3x + 2x − x + 3
3 2
−(3x − 9x )
3 2 6. Warm-up
Divide.
(3x + 2x − x + 3) ÷ (x − 3)
3 2
2
3x
x − 3 3x + 2x − x + 3
3 2
−(3x − 9x )
3 2
11x − x
2 7. Warm-up
Divide.
(3x + 2x − x + 3) ÷ (x − 3)
3 2
3x +11x
2
x − 3 3x + 2x − x + 3
3 2
−(3x − 9x )
3 2
11x − x
2 8. Warm-up
Divide.
(3x + 2x − x + 3) ÷ (x − 3)
3 2
3x +11x
2
x − 3 3x + 2x − x + 3
3 2
−(3x − 9x )
3 2
11x − x
2
−(11x − 33x)
2 9. Warm-up
Divide.
(3x + 2x − x + 3) ÷ (x − 3)
3 2
3x +11x
2
x − 3 3x + 2x − x + 3
3 2
−(3x − 9x )
3 2
11x − x
2
−(11x − 33x)
2
32x + 3 10. Warm-up
Divide.
(3x + 2x − x + 3) ÷ (x − 3)
3 2
3x +11x +32
2
x − 3 3x + 2x − x + 3
3 2
−(3x − 9x )
3 2
11x − x
2
−(11x − 33x)
2
32x + 3 11. Warm-up
Divide.
(3x + 2x − x + 3) ÷ (x − 3)
3 2
3x +11x +32
2
x − 3 3x + 2x − x + 3
3 2
−(3x − 9x )
3 2
11x − x
2
−(11x − 33x)
2
32x + 3
−(32x − 96) 12. Warm-up
Divide.
(3x + 2x − x + 3) ÷ (x − 3)
3 2
3x +11x +32
2
x − 3 3x + 2x − x + 3
3 2
−(3x − 9x )
3 2
11x − x
2
−(11x − 33x)
2
32x + 3
−(32x − 96)
99 13. Warm-up
Divide.
(3x + 2x − x + 3) ÷ (x − 3)
3 2
3x +11x +32
2
x − 3 3x + 2x − x + 3
3 2
−(3x − 9x )
3 2
3x + 11x + 32, R : 99
2
11x − x
2
−(11x − 33x)
2
32x + 3
−(32x − 96)
99 15. Rational Roots Theorem
Let p be all factors of the leading
coefficient and q be all factors of the
constant in any polynomial. Then
p/q gives all possible roots of the
polynomial. 19. Synthetic Division
Another way to divide polynomials, without the
use of variables
Only works if you’re dividing by a linear factor
Allows for us to test whether a possible root is an
actual zero 38. Example 1
Determine whether 1 is a root of
4x − 3x + x + 5
6 4 2
1 4 0 −3 0 1 0 5
4 4 1 1 2 2
4 4 1 1 2 2 7
4x + 4x + x + x + 2x + 2, R : 7
5 4 3 2 40. Example 2
Use synthetic division to find the quotient and
remainder.
(4x − 7x − 11x + 5) ÷ (4x − 5)
3 2
5
4x − 5 → x − 4 41. Example 2
Use synthetic division to find the quotient and
remainder.
(4x − 7x − 11x + 5) ÷ (4x − 5)
3 2
5
4x − 5 → x − 4
5
4
4 −7 −11 5 42. Example 2
Use synthetic division to find the quotient and
remainder.
(4x − 7x − 11x + 5) ÷ (4x − 5)
3 2
5
4x − 5 → x − 4
5
4
4 −7 −11 5
4 43. Example 2
Use synthetic division to find the quotient and
remainder.
(4x − 7x − 11x + 5) ÷ (4x − 5)
3 2
5
4x − 5 → x − 4
5
4
4 −7 −11 5
5
4 44. Example 2
Use synthetic division to find the quotient and
remainder.
(4x − 7x − 11x + 5) ÷ (4x − 5)
3 2
5
4x − 5 → x − 4
5
4
4 −7 −11 5
5
4 -2 45. Example 2
Use synthetic division to find the quotient and
remainder.
(4x − 7x − 11x + 5) ÷ (4x − 5)
3 2
5
4x − 5 → x − 4
5
4
4 −7 −11 5
5
5 −2
4 -2 46. Example 2
Use synthetic division to find the quotient and
remainder.
(4x − 7x − 11x + 5) ÷ (4x − 5)
3 2
5
4x − 5 → x − 4
5
4
4 −7 −11 5
5
5 −2
27
4 -2 − 2 47. Example 2
Use synthetic division to find the quotient and
remainder.
(4x − 7x − 11x + 5) ÷ (4x − 5)
3 2
5
4x − 5 → x − 4
5
4
4 −7 −11 5
5 135
5 −2 − 8
27
4 -2 − 2 48. Example 2
Use synthetic division to find the quotient and
remainder.
(4x − 7x − 11x + 5) ÷ (4x − 5)
3 2
5
4x − 5 → x − 4
5
4
4 −7 −11 5
5 135
5 −2 − 8
27 95
4 -2 − 2
− 8 49. Example 2
Use synthetic division to find the quotient and
remainder.
(4x − 7x − 11x + 5) ÷ (4x − 5)
3 2
5
4x − 5 → x − 4
5
4
4 −7 −11 5
5 135
5 −2 − 8
27 95
4 -2 − 2
− 8
27 95
4x − 2x −
2
2
,R:− 8 51. Example 3
Use synthetic division to find the quotient and
remainder.
(6x − 16x + 17x − 6) ÷ (3x − 2)
3 2
3x − 2 → x − 2
3 52. Example 3
Use synthetic division to find the quotient and
remainder.
(6x − 16x + 17x − 6) ÷ (3x − 2)
3 2
3x − 2 → x − 2
3
2
3 6 −16 17 −6 53. Example 3
Use synthetic division to find the quotient and
remainder.
(6x − 16x + 17x − 6) ÷ (3x − 2)
3 2
3x − 2 → x − 2
3
2
3 6 −16 17 −6
6 54. Example 3
Use synthetic division to find the quotient and
remainder.
(6x − 16x + 17x − 6) ÷ (3x − 2)
3 2
3x − 2 → x − 2
3
2
3 6 −16 17 −6
4
6 55. Example 3
Use synthetic division to find the quotient and
remainder.
(6x − 16x + 17x − 6) ÷ (3x − 2)
3 2
3x − 2 → x − 2
3
2
3 6 −16 17 −6
4
6 -12 56. Example 3
Use synthetic division to find the quotient and
remainder.
(6x − 16x + 17x − 6) ÷ (3x − 2)
3 2
3x − 2 → x − 2
3
2
3 6 −16 17 −6
4 -8
6 -12 57. Example 3
Use synthetic division to find the quotient and
remainder.
(6x − 16x + 17x − 6) ÷ (3x − 2)
3 2
3x − 2 → x − 2
3
2
3 6 −16 17 −6
4 -8
6 -12 9 58. Example 3
Use synthetic division to find the quotient and
remainder.
(6x − 16x + 17x − 6) ÷ (3x − 2)
3 2
3x − 2 → x − 2
3
2
3 6 −16 17 −6
4 -8 6
6 -12 9 59. Example 3
Use synthetic division to find the quotient and
remainder.
(6x − 16x + 17x − 6) ÷ (3x − 2)
3 2
3x − 2 → x − 2
3
2
3 6 −16 17 −6
4 -8 6
6 -12 9 0 60. Example 3
Use synthetic division to find the quotient and
remainder.
(6x − 16x + 17x − 6) ÷ (3x − 2)
3 2
3x − 2 → x − 2
3
2
3 6 −16 17 −6
4 -8 6
6 -12 9 0
6x − 12x + 9, R : 0
2 66. Factoring a Quadratic
Multiply a and c
Factor ac into two factors that add up to b
Replace b with these two values
Group first 2 and last 2 terms
Factor out the GCF of each 67. Factoring a Quadratic
Multiply a and c
Factor ac into two factors that add up to b
Replace b with these two values
Group first 2 and last 2 terms
Factor out the GCF of each
Factors: (Stuff inside)(Stuff outside) 68. Example 4
Factor.
a. 2x + x − 6
2
b. 4x − 19x + 12
2 69. Example 4
Factor.
a. 2x + x − 6
2
b. 4x − 19x + 12
2
2i−6 70. Example 4
Factor.
a. 2x + x − 6
2
b. 4x − 19x + 12
2
2i−6 = −12 71. Example 4
Factor.
a. 2x + x − 6
2
b. 4x − 19x + 12
2
2i−6 = −12
= 4(−3) 72. Example 4
Factor.
a. 2x + x − 6
2
b. 4x − 19x + 12
2
2i−6 = −12
= 4(−3)
2x + 4x − 3x − 6
2 73. Example 4
Factor.
a. 2x + x − 6
2
b. 4x − 19x + 12
2
2i−6 = −12
= 4(−3)
2x + 4x − 3x − 6
2
(2x + 4x) + (−3x − 6)
2 74. Example 4
Factor.
a. 2x + x − 6
2
b. 4x − 19x + 12
2
2i−6 = −12
= 4(−3)
2x + 4x − 3x − 6
2
(2x + 4x) + (−3x − 6)
2
2x(x + 2) − 3(x + 2) 75. Example 4
Factor.
a. 2x + x − 6
2
b. 4x − 19x + 12
2
2i−6 = −12
= 4(−3)
2x + 4x − 3x − 6
2
(2x + 4x) + (−3x − 6)
2
2x(x + 2) − 3(x + 2)
(x + 2)(2x − 3) 76. Example 4
Factor.
a. 2x + x − 6
2
b. 4x − 19x + 12
2
2i−6 = −12 4i12 = 48
= 4(−3)
2x + 4x − 3x − 6
2
(2x + 4x) + (−3x − 6)
2
2x(x + 2) − 3(x + 2)
(x + 2)(2x − 3) 77. Example 4
Factor.
a. 2x + x − 6
2
b. 4x − 19x + 12
2
2i−6 = −12 4i12 = 48
= 4(−3) = (−16)(−3)
2x + 4x − 3x − 6
2
(2x + 4x) + (−3x − 6)
2
2x(x + 2) − 3(x + 2)
(x + 2)(2x − 3) 78. Example 4
Factor.
a. 2x + x − 6
2
b. 4x − 19x + 12
2
2i−6 = −12 4i12 = 48
= 4(−3) = (−16)(−3)
2x + 4x − 3x − 6
2
4x − 16x − 3x + 12
2
(2x + 4x) + (−3x − 6)
2
2x(x + 2) − 3(x + 2)
(x + 2)(2x − 3) 79. Example 4
Factor.
a. 2x + x − 6
2
b. 4x − 19x + 12
2
2i−6 = −12 4i12 = 48
= 4(−3) = (−16)(−3)
2x + 4x − 3x − 6
2
4x − 16x − 3x + 12
2
(2x + 4x) + (−3x − 6)
2
(4x − 16x) + (−3x + 12)
2
2x(x + 2) − 3(x + 2)
(x + 2)(2x − 3) 80. Example 4
Factor.
a. 2x + x − 6
2
b. 4x − 19x + 12
2
2i−6 = −12 4i12 = 48
= 4(−3) = (−16)(−3)
2x + 4x − 3x − 6
2
4x − 16x − 3x + 12
2
(2x + 4x) + (−3x − 6)
2
(4x − 16x) + (−3x + 12)
2
2x(x + 2) − 3(x + 2) 4x(x − 4) − 3(x − 4)
(x + 2)(2x − 3) 81. Example 4
Factor.
a. 2x + x − 6
2
b. 4x − 19x + 12
2
2i−6 = −12 4i12 = 48
= 4(−3) = (−16)(−3)
2x + 4x − 3x − 6
2
4x − 16x − 3x + 12
2
(2x + 4x) + (−3x − 6)
2
(4x − 16x) + (−3x + 12)
2
2x(x + 2) − 3(x + 2) 4x(x − 4) − 3(x − 4)
(x + 2)(2x − 3) (x − 4)(4x − 3)