Honors Advanced Algebra Lesson 2-4

Warm-up Simplify each of the following x 2 / 5x 2. 36x 3 y / 3x 2 3. (5x x 2 ) / x Challenge: 36x 3 y / 3x 2 y 2

Dividing a Polynomial by a Monomial To divide a polynomial by a monomial, we have 2 options: place the monomial in the denominator and try to reduce each as a fraction or perform long division as we do with constants.

(Ex 1) Divide a polynomial by a monomial Divide (10x 3 – 25x x) by 5x. Method 1: Write the division as a fraction and divide each term by 5x.

(Ex 1) Divide a polynomial by a monomial Divide 10x 3 – 25x x by 5x. Method 2: Use long division.

Let’s Practice 1. Divide 12x 3 + 9x 2 – 3x by 3x. 2. Divide 6x 3 y + 24x 2 y xy 3 by 2xy

Dividing a polynomial by a binomial Divide 2x 2 + 9x – 6 by 2x + 3 using long division.

Let’s Practice 1. Divide x 2 + 8x + 15 by (x + 3) 2. Divide 3x 2 – x – 14 by (3x – 7). 2. Divide 6x 2 – 13x + 11 by (3x – 5).

(Ex 3) Insert missing terms. Divide 4x 2 – 11 by x. Step 1: Rewrite in standard form and fill in missing terms. Step 2: Divide using long division.

Checkpoint: Divide using long division. 5. Divide ( x 2 ) by (-3 + x). Before Dividing, always be sure to write everything in standard form and fill in any missing terms.

(Ex 4) Use Synthetic division. a) Divide x 2 + 3x – 10 by x + 5.

(Ex 5) Use Synthetic division. b) Divide 3x 2 – 12 by x – 2. Be sure to fill in any missing terms first.

Let’s Practice 4. Divide (6 – 2x + x 2 ) by (2 + x).

Homework Division WS (odds – long division evens – synthetic div.) P. 102, #13-24 (odds only)