UNIT 2, LESSON 3 POLYNOMIAL DIVISION Adapted by Mrs. King from

BLAST FROM THE PAST…

How many times does 5 go into 8?

BLAST FROM THE PAST… How many times does 5 go into 8?

BLAST FROM THE PAST… How many times does 5 go into 8?

BLAST FROM THE PAST… How many times does 5 go into 8? Subtract

BLAST FROM THE PAST… How many times does 5 go into 8? Subtract Bring down

ALGEBRAIC LONG DIVISION Divide (2x³ + 3x² - x + 1) by (x + 2)

ALGEBRAIC LONG DIVISION Divide (2x³ + 3x² - x + 1) by (x + 2) x + 2 is the divisor The quotient will be here. 2x³ + 3x² - x + 1 is the dividend

ALGEBRAIC LONG DIVISION First divide the first term of the dividend, 2x³, by x (the first term of the divisor). This gives 2x². This will be the first term of the quotient.

ALGEBRAIC LONG DIVISION Now multiply 2x² by x + 2 and subtract

ALGEBRAIC LONG DIVISION Bring down the next term, -x.

ALGEBRAIC LONG DIVISION Now divide –x², the first term of –x² - x, by x, the first term of the divisor which gives –x.

ALGEBRAIC LONG DIVISION Multiply –x by x + 2 and subtract

ALGEBRAIC LONG DIVISION Bring down the next term, 1

ALGEBRAIC LONG DIVISION Divide x, the first term of x + 1, by x, the first term of the divisor which gives 1

ALGEBRAIC LONG DIVISION Multiply x + 2 by 1 and subtract

ALGEBRAIC LONG DIVISION The remainder is –1. The quotient is 2x² - x + 1

Divide 125x by 5x - 2

SYNTHETIC DIVISION When the divisor (what we're dividing by) is of the form x-a, we can use synthetic division instead of long division to find the quotient and remainder.

SYNTHETIC DIVISION Divide by

SYNTHETIC DIVISION Place the opposite of the divisor to the left of the coefficients of the dividend

SYNTHETIC DIVISION Carry down the first coefficient

SYNTHETIC DIVISION Multiply by the divisor

SYNTHETIC DIVISION ADD!

SYNTHETIC DIVISION Continue to multiply by the divisor and ADD until you reach the end. *Box off the last answer! This is your remainder!

SYNTHETIC DIVISION Continue to multiply by the divisor and ADD until you reach the end. *Box off the last answer! This is your remainder! These are the coefficients of your answer!

SYNTHETIC DIVISION To find the polynomial form of the quotient, start with an exponent one-degree smaller than the original dividend

SYNTHETIC DIVISION To find the polynomial form of the quotient, start with an exponent one-degree smaller than the original dividend