Synthetic Division in Color.notebook
Synthetic Division
Explained in COLOR
Divide the following with Synthetic Division:
x3 ­ 19x ­ 30
x + 3
Then find all the factors and the
solutions for the polynomial
1
Synthetic Division in Color.notebook
x + 3
Divisor
x + 3 = 0
x = ­3
Set the divisor equal to zero
and solve
Don't forget the place holder!!!
x3 + 0x2 ­ 19x ­ 30
­ 3
1 0 ­19 ­30
Remove the variables;
Use only the coefficients
­ 3
1 0 ­19 ­30
1
Bring down the first term
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Synthetic Division in Color.notebook
­ 3
1 0 ­19 ­30
-3
1
Multiply -3(1)
­ 3
1 0 ­19 ­30
-3
1
-3
Combine terms -3 and 0
3
Synthetic Division in Color.notebook
­ 3
1 0 ­19 ­30
9
-3
1
-3
Multiply -3 and -3
­ 3
1 0 ­19 ­30
9
-3
1
-3
-10
Combine terms -19 and 9
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Synthetic Division in Color.notebook
­ 3
1 0 ­19 ­30
9 30
-3
1 -3 -10
Multiply -3 and -10
­ 3
1 0 ­19 ­30
9 30
-3
0
1 -3 -10
Combine -30 and 30
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Synthetic Division in Color.notebook
­ 3
1 0 ­19 ­30
9 30
-3
0
1 -3 -10
x2 - 3x - 10
Starting on the right and moving left:
the numbers represent the remainder,
constant, x term, x2 term, x3 term, etc.
x3 ­ 19x ­ 30
= x2 - 3x - 10
x + 3
x3 ­ 19x ­ 30
So you have found 2 factors of
(x + 3) (x2 ­ 3x ­ 10) = x3 + 0x2 ­ 19x ­ 30
Are there more?
(x + 3) (x ­ 5) (x + 2)
x = - 3, 5, -2
Factors of the Polynomial
Solutions of the Polynomial
6