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

Dividing Polynomials Monday, February 2, 2015

Long Division For Polynomials

Divide a Polynomial by a Monomial  The 1 st way may be what you are used to seeing. The 2 nd way is written like a rational function. Just like fractions, we can split it up. Then we can follow the rules of exponents.  6xy 2 - 3xy + 2x 2 y xy xy xy  6y x Ex: (6xy 2 – 3xy + 2x 2 y) ÷ xy Is the same as: 6xy 2 – 3xy + 2x 2 y xy

You Try  (5ab 2 – 4ab + 7a 2 b) (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. (x 2 – 10x – 24 ) ÷ (x + 2) 2. (8x 4 – 4x 2 + x +4) ÷ (2x + 1) 3. (x 3 + y 3 ) ÷ (x + y)

You Try  1. (3a 4 – 6a 3 – 2a 2 + a – 6) ÷ (a + 1)  2. (t 2 + 3t – 9) ÷ (5 – t ) Hint: reorder the denominator  3. (3x 3 – 5x x – 3) ÷ (3x + 1)

Synthetic Division For 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. (5x 3 – 13x x – 8) ÷ (x – 2) 2. (x x 2 – 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. (b 4 – 2b 3 + b 2 – 3b + 2) ÷ (b – 2)  2. (x 2 – 4x + 6) ÷ (x – 3)

Polynomial Division Worksheet Classwork (1-10) Homework (11-20) (subject to change)

Exit Ticket 1. By a show of hands, who prefers synthetic division? 2. Why?