Thursday, October 10, 2019

3.5 Dividing Polynomials

Polynomials can be divided in the same manner as numbers. We're going to learn polynomial division (long division) and synthetic division (the short form of polynomial division).

A Quick Vocabulary Review: remainder quotient 21 5 ) 107 dividend 10 divisor 07 5 2

In general, a polynomial can be divided by a polynomial of the same degree or less. Why?

It is important to: - arrange terms in descending order of degree in both the divisor and the dividend;

- use zero as the coefficient for any missing powers.

If you finish dividing and the remainder is zero, then the divisor and the quotient are factors of the dividend. 1) Polynomial (Long) Division

3 2 Calculate (x + 2x - 6x + 1) ÷ (x + 2) using long division. To carry out long division with polynomials: • Place your divisor outside the long division bracket. • Place your dividend within the bracket. • Look at the first term of your divisor and determine the number of times it can go in to the first term in the dividend - write this on top, then multiply the divisor by the value on top. • Subtract the product from the dividend. • Repeat this until you cannot simplify any further.

More Practice with Long Division

Calculate each of the following.

4 3 2 2 5 4 2 a) (x + 3x - 2x + 5x - 1) ÷ (x + 7) b) (x + 4x + 9x + 8)÷(x - 2x +3)

3) Finding a Missing Component of a Division Question

You will often be given all but one of the divisor, dividend, quotient, and remainder and asked to find the missing information. A few key things to remember when this happens are:

1) The remainder has to be added to the product of the divisor and quotient to get the proper dividend. ex/ Find the dividend in the given situation.

divisor: 3x - 2 quotient: x3 + x -12 remainder: 15

2) If you are asked to find the remainder, you just need to divide. 3) If you are asked to decide if the divisor or quotient is a factor of the equation, you are looking for a remainder of zero.