Warm-up over Lesson 5-1.

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Presentation transcript:

Warm-up over Lesson 5-1

Simplify b2 ● b5 ● b3. A. b5 B. b8 C. b10 D. b30 5-Minute Check 1

A. B. C. D. 5-Minute Check 2

Simplify (10a2 – 6ab + b2) – (5a2 – 2b2). A. 15a2 + 8ab + 3b2 B. 10a2 – 6ab – b2 C. 5a2 + 6ab – 3b2 D. 5a2 – 6ab + 3b2 5-Minute Check 3

Simplify 7w(2w2 + 8w – 5). A. 14w3 + 56w2 – 35w B. 14w2 + 15w – 35 C. 9w2 + 15w – 12 D. 2w2 + 15w – 5 5-Minute Check 4

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 5-Minute Check 6

Chapter 5 Lesson 2 (Part A) Dividing Polynomials Long Division

Mathematical Practices 6 Attend to precision. 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. CCSS

Divide polynomials using long division. You divided monomials. Divide polynomials using long division. Then/Now

Example # 1 = a – 3b2 + 2a2b3 a1 – 1 = a0 or 1 and b1 – 1 = b0 or 1 Divide a Polynomial by a Monomial Sum of quotients Divide. = a – 3b2 + 2a2b3 a1 – 1 = a0 or 1 and b1 – 1 = b0 or 1 Answer: a – 3b2 + 2a2b3 Example 1

Example #2 Simplify

Example #3 Simplify

A. 2x3y – 3x5y2 B. 1 + 2x3y – 3x5y2 C. 6x4y2 + 9x7y3 – 6x9y4 D. 1 + 2x7y3 – 3x9y4 Example 1

Remembering Long Division……

Example # 4 Use long division to find (x2 – 2x – 15) ÷ (x – 5). Division Algorithm Use long division to find (x2 – 2x – 15) ÷ (x – 5). x(x – 5) = x2 – 5x 3(x – 5) = 3x – 15 –2x – (–5x) = 3x Answer: The quotient is x + 3. The remainder is 0. Example 2

Example # 5 Use long division to find the quotient.

Example # 6 Use long division to find the quotient.

Example # 7 Use long division to find the quotient.

Use long division to find (x2 + 5x + 6) ÷ (x + 3). A. x + 2 B. x + 3 C. x + 2x D. x + 8 Example 2

Example # 8 Which expression is equal to (a2 – 5a + 3)(2 – a)–1? Divide Polynomials Which expression is equal to (a2 – 5a + 3)(2 – a)–1? A a + 3 B C D Example 3

Divide Polynomials Read the Test Item Since the second factor has an exponent of –1, this is a division problem. Solve the Test Item 3(–a + 2) = –3a + 6 –a(–a + 2) = a2 – 2a Rewrite 2 – a as –a + 2. –5a – (–2a) = –3a Subtract. 3 – 6 = –3 Example 3

The quotient is –a + 3 and the remainder is –3. Divide Polynomials The quotient is –a + 3 and the remainder is –3. Therefore, . Answer: The answer is D. Example 3

Which expression is equal to (x2 – x – 7)(x – 3)–1? B. C. D. Example 3

Pg . 315: 1-7 and 12-25 all

Reflection…… If a polynomial is divided by a binomial and the remainder is 0, what does this tell you about the relationship between the binomial and the polynomial? End of the Lesson