1. Aims: To recap the remainder and factor theorems. To be able to divide a polynomial by another polynomial using your preferred method To understand terminology, quotient and remainder. Algebra - Long Division Lesson 2

2. Improper fractions and mixed numbers Remember, a numerical fraction is called an improper fraction if the numerator is larger than the denominator and we can change them to a mixed number. For example, Now ___ is the quotient and ___ is the remainder. An algebraic fraction is called an improper fraction when the numerator is a polynomial of degree greater than, or equal to, the degree of the denominator and in general is written as:

3. Write in the form A +. Rewriting the numerator A useful technique for writing improper fractions in proper form is to look for ways to rewrite the numerator so that part of it can be divided by the denominator. For example,

4. Rewriting the numerator We can write this in fraction form as: So when 3 x 2 + 2 x is divided by x 2 + 1 the quotient is ___ and the remainder is _________. What is the quotient and the remainder when 3 x 2 + 2 x is divided by x 2 + 1?

5. Constructing an identity When the numerator cannot easily be manipulated we can use long division. For example What is x 3 – 4 x 2 + 5 divided by x 2 – 3? x 3 – 4 x 2 + 0 x + 5 x 2 – 3 The quotient is and the remainder is so,

6. What is x 4 + 2x 3 – 4 x 2 + 5 divided by x 2 – 4x ? Long Division

7. What is x 4 + 3x 3 – 2x + 6 divided by x 2 + 2x ? On w/b Do Ex B page 21