Section 4.2
Dividing Polynomials
Long Division of Polynomials
Recall: Divided = Quotient*Divisor + Remainder. If the Remainder = 0, then the
quotient is said to be a factor of the dividend.
Example 1: Divide.
a.
b.
Section 4.2 – Dividing Polynomials
1
Dividing Polynomials Using Synthetic Division
We can use synthetic division to divide polynomials if the divisor is of the form x  c.
Example 2: Divide.
a.
b.
The Remainder Theorem
If the polynomial P(x) is divided by x – c, then the remainder is P(c).
Example 3: Use synthetic division and the Remainder Theorem to evaluate P(-4) for
x
2
2
11x
100
Section 4.2 – Dividing Polynomials
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Example 4: Use synthetic division and the Remainder Theorem to evaluate P(2) for
x
4
9
8
5
2
3
2
Example 5: Determine if (x + 2) is a factor of P( x )  x  6x  3x  10 .
Example 6: Find a polynomial of degree 3 that has zeros 3, 2
Section 4.2 – Dividing Polynomials
4.
3