Warm-Up Use long division to divide 5 into 3462. - - -

Warm-Up Use long division to divide 5 into 3462. Quotient Divisor Dividend - - - Remainder

Warm-Up Use long division to divide 5 into 3462. Dividend Remainder Divisor Divisor Quotient

Remainders If you are lucky enough to get a remainder of zero when dividing, then the divisor divides evenly into the dividend This means that the divisor is a factor of the dividend. For example, when dividing 3 into 192, the remainder is 0. Therefore, 3 is a factor of 192.

5-3 Dividing Polynomials Skills: Divide polynomials using long division. Divide polynomials using synthetic division. Glencoe – Algebra 2 Chapter 5: Polynomials

Vocabulary As a group, define each of these without your book. Give an example of each word and leave a bit of space for additions and revisions. Quotient Remainder Dividend Divisor Divides Evenly Factor

Two Types of Polynomial Division Polynomial Long Division Synthetic Division Always works Use the normal algorithm for long division Divisor MUST be in the form (x – r) x cannot be raised to any power other than one to use synthetic division!

Polynomial Long Division remainder divisor divisor quotient Make sure both the polynomial and divisor are in standard form. (decreasing order of degree) If terms are missing, put them in with 0 coefficients. The polynomial goes inside the house and the divisor goes outside. (like regular long division) Focus on the first term and what you’d have to multiply the first term of the divisor by to get the first term of the polynomial. Continue multiplying and subtracting like regular long division until the remainder is one degree less than the divisor. Glencoe – Algebra 2 Chapter 5: Polynomials

Example 1 Divide 497 by 8. Glencoe – Algebra 2 Chapter 5: Polynomials

Simplify: Rewrite as follows: Change the signs. Change the signs. Scrap Paper Change the signs. Ask yourself…x times what gives 2x3? Scrap Paper Scrap Paper Now ask yourself…x times what gives 3x2? Answer…x times 2x2 gives 2x3. Answer…x times 3x gives 3x2. Now ask yourself…x times what gives -2x? Answer…x times -2 gives -2x.

Important Stuff to Remember!! Your exponents must go in descending order. If you are missing an exponent, put in a zero for that place. Example: You must change signs before you add!!! Write remainders as fractions.

One last example Glencoe – Algebra 2 Chapter 5: Polynomials

Try these:

Synthetic Division Getting the problem set up. -3 3 7 0 1 -11 First, make sure there are no skipped powers. Rewrite with zeros if necessary. Next, write just the coefficients of the dividend. -3 3 7 0 1 -11 Then, find out what value makes the divisor equal zero and write that number in the “box”. Finally, skip a line and draw a line.

Getting’ it done. -3 3 7 0 1 -11 -9 6 -18 51 3 -2 6 -17 40 3 7 0 1 -11 x x x x -9 6 -18 51 3 -2 6 -17 40 1. Bring down the first number. 2. Multiply the number in the “box” by this number. 3. Place your answer under the next number. 4. Add. 5. Repeat 2-4.

Now what?!? -3 3 -9 -2 6 -18 -17 51 40 3 7 0 1 -11 Box your last number. This is your remainder. Your first variable’s exponent will be one less than the dividend’s. The remaining exponents go in descending order.

Example 3 Glencoe – Algebra 2 Chapter 5: Polynomials

Example 4 Glencoe – Algebra 2 Chapter 5: Polynomials

The Synthetic Division Shuffle and Add! and Add! and Add! and Add! Multiply, Multiply, Multiply, Multiply,

Try these Divide using synthetic division

Synthetic Division

Class/Homework Handout Oh yes, and one more thing (next slide…)

Dividing a Polynomial by a Monomial Divide each term of the polynomial by the monomial. Remember to divide coefficients and subtract exponents.

Divide 12x2 – 20x + 8 by 4x 12x2 – 20x + 8 4x 4x 4x

Examples Divide 9x2 + 12x – 18 by 3x. (Do in your notes) Divide 32x2 – 16x + 64 by -8x

Practice Answers: Divide 18x2 + 45x – 36 by 9x Divide 10b3 – 8b2 -5b by – 2b Divide x2 – 8x + 15 by x – 3 Divide 5x2 + 3x – 15 by x + 2