Dividing Polynomials

Dividing Polynomials Honors Advanced Algebra Lesson 2-4

Warm-up • Simplify each of the following. • 25x2 / 5x • 36x3y / 3x2 • (5x2 + 12x2) / x Challenge: 36x3y / 3x2y2

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 (10x3– 25x2 + 15x) 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 10x3 – 25x2 + 15x by 5x. Method 2: Use long division.

Let’s Practice • Divide 12x3 + 9x2 – 3x by 3x. • Divide 6x3y + 24x2y2 + 12xy3 by 2xy

Dividing a polynomial by a binomial Divide 2x2 + 9x – 6 by 2x + 3 using long division.

Let’s Practice • Divide x2 + 8x + 15 by (x + 3) • Divide 3x2 – x – 14 by (3x – 7). • Divide 6x2 – 13x + 11 by (3x – 5).

(Ex 3) Insert missing terms. Divide 4x2 – 11 by -3 + 2x. Step 1: Rewrite in standard form and fill in missing terms. Step 2: Divide using long division.

Checkpoint: Divide using long division. 5. Divide (-11 + 3x2) 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 x2 + 3x – 10 by x + 5.

(Ex 5) Use Synthetic division. • Divide 3x2 – 12 by x – 2. Be sure to fill in any missing terms first.

Let’s Practice 4. Divide (6 – 2x + x2) by (2 + x).

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

Dividing Polynomials