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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.