1. Dividing Polynomials 3𝑥+5 𝑥+2 | 3 𝑥 2 +11𝑥+10 Quotient Divisor
𝑥+2 | 3 𝑥 2 +11𝑥+10
Quotient
Divisor
Dividend

2. Divide
2466 7

3. Dividing Polynomials 𝑥 2 +3𝑥 − 8 𝑥+2 Long division
Write as a long division problem.
Focusing on the front term, figure out what you need to multiply by to get the first term of the polynomial
Write that on top of the “house” and multiply it through to the divisor
Subtract the resulting expression
Repeat the process until you get to the end of the dividend
If there is a remainder, write that as a fraction.
𝑥 2 +3𝑥 − 8 𝑥+2

4. You Try:
4 𝑥 2 −5𝑥+8 𝑥 ) 3 𝑥 2 −7𝑥+12 𝑥 −5

5. This can ONLY be done when divisor is x ± c
Dividing Polynomials
synthetic division
This can ONLY be done when divisor is x ± c
Write the OPPOSITE of the divisor’s constant on the outside of a vertical line |
Write the COEFFICIENTS of the dividend next to that (keep the signs)
Drop the first dividend number, multiply that by the divisor number and place under the next coefficient
Add the two numbers and write the result under that, repeat the process of multiplying and adding until you get to the end of the polynomial
Write the results as the quotient, the last value is the remainder.
𝑥 2 +3𝑥 −4 𝑥+2

6. You Try:
7 𝑥 2 −6𝑥+1 𝑥 −3 2) 8 𝑥 2 −12𝑥 −17 𝑥+7

7. Also, x – a is a FACTOR of p(x) if f(a) = 0
Remainder Theorem:
For a given a polynomial, p(x), the remainder when dividing by x – a [a is a constant] will be equal to p(a). [the value of the polynomial when you substitute a in for x]
Also, x – a is a FACTOR of p(x) if f(a) = 0
[remainder is zero]
Example: Determine if x + 2 is a FACTOR of 2x2 – 3x + 5.