FiveMinute Check over Lesson 11 4 CCSS ThenNow

Over Lesson 11– 4 During the summer months, the glaciers of Mount Rainier move

Mathematical Practices 8 Look for and express regularity in repeated reasoning. Common Core State

You divided rational expressions. • Divide a polynomial by a monomial. • Divide a

Divide Polynomials by Monomials A. Find (4 x 2 – 18 x) ÷ 2

Divide Polynomials by Monomials B. Find (2 y 2 – 3 y – 9)

Divide a Polynomial by a Binomial Find (2 r 2 + 5 r –

Use Long Division Find (x 2 + 7 x – 15) ÷ (x –

Use Long Division Step 2 Divide the first term of the partial dividend, 9

Use Long Division Answer: So, (x 2 + 7 x – 15) ÷ (x

Divide Polynomials to Solve a Problem GEOMETRY The area of a rectangle is represented

GEOMETRY The area of a triangle is represented by 8 x + 21. The

Insert Missing Terms Find (x 3 – 34 x + 45) ÷ (x –

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Five-Minute Check (over Lesson 11– 4) CCSS Then/Now Example 1: Divide Polynomials by Monomials Example 2: Divide a Polynomial by a Binomial Example 3: Use Long Division Example 4: Real-World Example: Divide Polynomials to Solve a Problem Example 5: Insert Missing Terms

Over Lesson 11– 4 A. B. C. D.

Over Lesson 11– 4 A. B. C. 1 D. x + 2

Over Lesson 11– 4 A. B. C. y 2 + 7 D. 1

Over Lesson 11– 4 During the summer months, the glaciers of Mount Rainier move about 18 inches per day. How many feet per hour do they move? A. B. C. D.

Over Lesson 11– 4 A. B. C. D.

Mathematical Practices 8 Look for and express regularity in repeated reasoning. Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

You divided rational expressions. • Divide a polynomial by a monomial. • Divide a polynomial by a binomial.

Divide Polynomials by Monomials A. Find (4 x 2 – 18 x) ÷ 2 x. Write as a rational expression. Divide each term by 2 x. Divide out common factors. = 2 x – 9 Answer: 2 x – 9 Simplify.

Divide Polynomials by Monomials B. Find (2 y 2 – 3 y – 9) ÷ 3 y. Write as a rational expression. Divide each term by 3 y. Divide out common factors. Simplify.

Divide Polynomials by Monomials Answer:

A. Find (48 z 2 + 18 z) ÷ 6 z. A. 8 z + 18 z B. 8 z + 18 C. 8 z + 3 D. 42 z + 12

B. Find (– 8 x 2 + 6 x – 28) ÷ 4 x. A. B. C. D.

Divide a Polynomial by a Binomial Find (2 r 2 + 5 r – 3) ÷ (r + 3). Write as a rational expression. Factor the numerator. Divide out common factors. = 2 r – 1 Answer: 2 r – 1 Simplify.

Use Long Division Find (x 2 + 7 x – 15) ÷ (x – 2) by using long division. Step 1 Divide the first term of the dividend, x 2, by the first term of the divisor, x. x 2 ÷ x = x Multiply x and x – 2. Subtract and bring down – 15.

Use Long Division Step 2 Divide the first term of the partial dividend, 9 x – 15, by the first term of the divisor, x. 9 x ÷ x = 9 Subtract and bring down – 15. Multiply 9 and x – 2. Subtract.

Use Long Division Answer: So, (x 2 + 7 x – 15) ÷ (x – 2) is x + 9 with a remainder of 3, which can be written as

Find (y 2 – 4 y + 5) ÷ (y – 3) by using long division. A. y – 2 B. y – 1 C. y + 5 D. y – 1

Divide Polynomials to Solve a Problem GEOMETRY The area of a rectangle is represented by 3 x + 90. Its length is (x – 3). Find (3 x + 90) ÷ (x – 3) to determine the width of the rectangle. 3 (–) 3 x – 9 99 Answer: So, rectangle. represents the width of the

GEOMETRY The area of a triangle is represented by 8 x + 21. The height is 2 x + 3. Find 2(8 x + 21) ÷ (2 x + 3) to find the base of the triangle. A. B. C. D.

Insert Missing Terms Find (x 3 – 34 x + 45) ÷ (x – 5). Insert an x 2 -term that has a coefficient of 0. (–) x 3 – 5 x 2 – 34 x (–) 5 x 2 – 25 x – 9 x + 45 (–) – 9 x + 45 0 Multiply x 2 and x – 5. Subtract and bring down 34 x. Multiply 5 x and x – 5. Subtract and bring down 45. Multiply – 9 and x – 5. Subtract. Answer: The quotient is x 2 + 5 x – 9.

Find (b 3 – 6 b 2 + 32) ÷ (b – 4). A. b 2 – 2 b – 8 B. b – 8 C. b 2 – 8 D. b 2