Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Five-Minute Check (over Lesson 5–1) CCSS Then/Now New Vocabulary Example 1: Divide a Polynomial by a Monomial Example 2: Division Algorithm Example 3: Standardized Test Example: Divide Polynomials Key Concept: Synthetic Division Example 4: Synthetic Division Example 5: Divisor with First Coeffecient Other than 1 Over Lesson 5–1 Simplify b2 ● b5 ● b3. Simplify (10a2 – 6ab + b2) – (5a2 – 2b2). Simplify 7w(2w2 + 8w – 5). State the degree of 6xy2 – 12x3y2 + y4 – 26. Find the product of 3y(2y2 – 1)(y + 4). Over Lesson 5–1 Simplify b2 ● b5 ● b3. A. b5 B. b8 C. b10 D. b30 Over Lesson 5–1 A. B. C. D. Over Lesson 5–1 Simplify (10a2 – 6ab + b2) – (5a2 – 2b2). A. 15a2 + 8ab + 3b2 B. 10a2 – 6ab – b2 C. 5a2 + 6ab – 3b2 D. 5a2 – 6ab + 3b2 Over Lesson 5–1 Simplify 7w(2w2 + 8w – 5). A. 14w3 + 56w2 – 35w B. 14w2 + 15w – 35 C. 9w2 + 15w – 12 D. 2w2 + 15w – 5 Over Lesson 5–1 State the degree of 6xy2 – 12x3y2 + y4 – 26. A. 11 B. 7 C. 5 D. 4 Over Lesson 5–1 Find the product of 3y(2y2 – 1)(y + 4). A. 18y5 + 72y4 – 9y3 – 36y2 B. 6y4 + 24y3 – 3y2 – 12y C. –18y3 – 3y2 + 12y D. 6y3 – 2y + 4 Content Standards A.APR.6 Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. Mathematical Practices 6 Attend to precision. You divided monomials. • Divide polynomials using long division. • Divide polynomials using synthetic division. • synthetic division Divide a Polynomial by a Monomial = a – 3b2 + 2a2b3 Answer: a – 3b2 + 2a2b3 A. 2x3y – 3x5y2 B. 1 + 2x3y – 3x5y2 C. 6x4y2 + 9x7y3 – 6x9y4 D. 1 + 2x7y3 – 3x9y4 Division Algorithm Use long division to find (x2 – 2x – 15) ÷ (x – 5). Answer: The quotient is x + 3. The remainder is 0. Use long division to find (x2 + 5x + 6) ÷ (x + 3). A. x + 2 B. x + 3 C. x + 2x D. x + 8 Divide Polynomials Which expression is equal to (a2 – 5a + 3)(2 – a)–1? A a+3 B C D Divide Polynomials Which expression is equal to (a2 – 5a + 3)(2 – a)–1? 2 − 5𝑎 + 3 𝑎 𝑎2 − 5𝑎 + 3 2 − 𝑎 −1 = 2−𝑎 = 𝑎2 − 5𝑎 + 3 ÷ 2 − 𝑎 The quotient is –a + 3 and the remainder is –3. 𝑎2 − 5𝑎 + 3 2 − 𝑎 −1 3 3 = −𝑎 + 3 + = −𝑎 + 3 − 𝑎−2 2−𝑎 Which expression is equal to (x2 – x – 7)(x – 3)–1? A. B. C. D. Synthetic Division Use synthetic division to find (x3 – 4x2 + 6x – 4) ÷ (x – 2). Step 1 x3 – 4x2 + 6x – 4 1 –4 Step 2 Step 3 Answer: 6 1 -4 6 2 -4 1 -2 2 1 -2 2 x2 – 2x + 2. –4 -4 4 0 Use synthetic division to find (x2 + 8x + 7) ÷ (x + 1). A. x + 9 B. x + 7 C. x + 8 D. x + 7 Divisor with First Coefficient Other than 1 Use synthetic division to find (4y3 – 6y2 + 4y – 1) ÷ (2y – 1). 4𝑦 3 − 6𝑦 2 + 4𝑦 − 1 4𝑦 3 − 6𝑦 2 + 4𝑦 − 1 1 4𝑦 3 − 6𝑦 2 + 4𝑦 − 1 = = • 1 1 2 2𝑦 − 1 2 𝑦− 𝑦− 2 1 2 4 4 −6 2 −4 4 −2 2 −1 0 0 So 4𝑦 3 − 6𝑦 2 + 4𝑦 − 1 1 = 4𝑦 2 − 4𝑦 + 2 2𝑦 − 1 2 = 2𝑦 2 − 2𝑦 + 1 2 Use synthetic division to find (8y3 – 12y2 + 4y + 10) ÷ (2y + 1). A. B. C. D.