Bell Ringer

In elementary school, you learned long division. Describe, in detail, how to divide 232 by 4 without a calculator.

Dividing Polynomials

Tuesday, September 16, 2014

Long DivisionFor Polynomials

Divide a Polynomial by a Monomial

The 1st way may be what you are used to seeing. The 2nd way is written like a rational function. Just like fractions, we can split it up. Then we can follow the rules of exponents.

6xy2 - 3xy + 2x2y

xy xy xy

6y -3 + 2x

Ex: (6xy2 – 3xy + 2x2y)

÷xy

Is the same as:

6xy2 – 3xy + 2x2yxy

You Try

(5ab2 – 4ab + 7a2b) (ab)-1

Hint – First make the negative exponent positive.

Divide a Polynomial by a Binomial

Just like in elementary school…

Divide Multiply Subtract Bring Down If there is a

remainder… write it as a fraction.

Like with decimals, you may need a placeholder.

Ex: 1. (x2 – 10x – 24 ) ÷ (x

+ 2)

2. (8x4 – 4x2 + x +4) ÷ (2x + 1)

3. (x3 + y3) ÷ (x + y)

You Try 1. (3a4 – 6a3 – 2a2 + a – 6) ÷ (a +

1)

2. (t2 + 3t – 9) ÷ (5 – t ) Hint: reorder the denominator

3. (3x3 – 5x2 + 10x – 3) ÷ (3x + 1)

Synthetic DivisionFor Polynomials

Divide a Polynomial by a Binomial

You can only use synthetic division when dividing by a binomial that is of degree 1 with a coefficient of 1.

IF the coefficient is not 1, you can divide the polynomial and binomial by the coefficient and then use synthetic division, but it’s messy, so you might as well use long division.

Ex: 1. (5x3 – 13x2 + 10x – 8) ÷ (x – 2)

2. (x3 + 13x2 – 12x – 8) ÷ (x + 2)

1. Write the coefficients.

2. Put the opposite of the constant of the divisor in the box.

3. Bring down, multiply, add, repeat.

4. Write your answer (1 degree less than the dividend).

You Try

1. (b4 – 2b3 + b2 – 3b + 2) ÷ (b – 2)

2. (x2 – 4x + 6) ÷ (x – 3)

ClassworkAlgebra II book p. 236-237 #16-54 even

HomeworkPolynomial Division Worksheet

Exit Ticket1. By a show of hands, who prefers synthetic division?2. Why?