Warm-up over Lesson 5-1

A. b5

B. b8

C. b10

D. b30

Simplify b2 ● b5 ● b3.

A.

B.

C.

D.

A. 15a2 + 8ab + 3b2

B. 10a2 – 6ab – b2

C. 5a2 + 6ab – 3b2

D. 5a2 – 6ab + 3b2

Simplify (10a2 – 6ab + b2) – (5a2 – 2b2).

A. 14w3 + 56w2 – 35w

B. 14w2 + 15w – 35

C. 9w2 + 15w – 12

D. 2w2 + 15w – 5

Simplify 7w(2w2 + 8w – 5).

A. 18y5 + 72y4 – 9y3 – 36y2

B. 6y4 + 24y3 – 3y2 – 12y

C. –18y3 – 3y2 + 12y

D. 6y3 – 2y + 4

Find the product of 3y(2y2 – 1)(y + 4).

Chapter 5 Lesson 2 (Part A)

Dividing Polynomials Long Division

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 a Polynomial by a Monomial

Answer: a – 3b2 + 2a2b3

Sum of quotients

Divide.

= a – 3b2 + 2a2b3 a1 – 1 = a0 or 1 and b1 – 1 = b0 or 1

Example # 1

)4()41620( 224 cdfcdfcdffdc

Example #2 Simplify

Example #3 Simplify 1232 )3)(2718( xyzyxyx

A. 2x3y – 3x5y2

B. 1 + 2x3y – 3x5y2

C. 6x4y2 + 9x7y3 – 6x9y4

D. 1 + 2x7y3 – 3x9y4

Remembering Long Division……

10878

Division Algorithm

Use long division to find (x2 – 2x – 15) ÷ (x – 5).

Answer: The quotient is x + 3. The remainder is 0.

–2x – (–5x) = 3x3(x – 5) = 3x – 15

x(x – 5) = x2 – 5x

Example # 4

Use long division to find the quotient.

)3()307( 2 xxx

Example # 5

Use long division to find the quotient.

)7()49( 2 xx

Example # 6

Use long division to find the quotient.

)2()206( 2 xxx

Example # 7

A. x + 2

B. x + 3

C. x + 2x

D. x + 8

Use long division to find (x2 + 5x + 6) ÷ (x + 3).

Which expression is equal to (a2 – 5a + 3)(2 – a)–1?

A a + 3

B

C

D

Divide Polynomials

Example # 8

Read the Test Item

Since the second factor has an exponent of –1, this is a division problem.

Solve the Test Item

Rewrite 2 – a as –a + 2.

–a(–a + 2) = a2 – 2a–5a – (–2a) = –3a3(–a + 2) = –3a + 6Subtract. 3 – 6 = –3

Divide Polynomials

The quotient is –a + 3 and the remainder is –3.

Answer: The answer is D.

Therefore, .

Divide Polynomials

Which expression is equal to (x2 – x – 7)(x – 3)–1?

A.

B.

C.

D.

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?