Name: __________________________________________
Hon Int Math 2 Handout (Sec.11-1 thru 11-2)
What is the degree of each monomial?
1
7m 6 n 5
3
5x7
2
5x6 y3
4
–9
6
2x7 – 8x7
What is the sum or difference?
5
6x7 + 8x7
Write the polynomial in standard form. Then name the polynomial based on its degree and
number of terms.
7
8
2 – 11x2 – 8x + 6x2
1
4g – 5g 3 + 9g 2 – 6
Name: ______________________
9
ID: A
A biologist studied the populations of white-sided jackrabbits and black-tailed jackrabbits over
a 5-year period. The biologist modeled the populations, in thousands, with the following
polynomials where x is time, in years.
2
White-sided jackrabbits: 9.7x − 0.8x + 2.3
2
Black-tailed jackrabbits: −1.1x + 7.7x + 5.4
What polynomial models the total number of white-sided and black-tailed jackrabbits?
2
a
−8.6x + 6.9x − 7.7
b
8.6x + 6.9x + 7.7
2
2
c
8.6x − 6.9x − 7.7
d
8.6x − 6.9x + 7.7
2
Simplify the sum.
10 (4u 3 + 3u 2 + 7) + (2u 3 – 7u + 8)
Simplify the difference.
11 (–7x – 5x4 + 5) – (–7x4 – 5 – 9x)
12 (4w2 – 7w – 6) – (8w2 + 2w – 3)
Simplify the product.
13 2n(n 2 + 3n + 4)
14 5a 2 (3a 4 + 3b + 2)
2
Name Class Date Standardized Test Prep
Adding and Subtracting Polynomials
Multiple Choice
For Exercises 1–6, choose the correct letter.
1. What is the degree of the monomial 3x 2y 3 ?
A. 2
B. 3
C. 5
D. 6
2. What is the simplified form of 8b3c2 + 4b3c2 ?
G. 12b3c2
F. 12bc
H. 12b6c4
I. 12b9c4
3. How is 6d - 8 + 4d 2 written in standard form?
A. 4d 2 + 6d - 8
B. 4d 2 + 6d + 8
C. 4d 2 - 6d - 8
D. 4d 2 - 6d + 8
4. What is the simplified form of (4j 2 + 6) + (2j 2 - 3)?
F. 6j 2 - 3
G. 6j 2 + 3
H. 6j 2 + 9
I. 4j 4 + 3
5. What is the difference of the following polynomials?
6x3 - 2x2 + 4
- (2x3 + 4x2 - 5)
A. 4x 3 - 2x2 - 1
B. 8x 3 + 6x2 - 1
C. 4x 3 - 2x2 + 1
D. 4x 3 - 6x2 + 9
6. What is the simplified form of (3x 2 - 4x + 6x) + (5x 3 + 2x 2 - 3x) in
standard form?
F. 5x 3 + 10x 2 - x
G. 8x 3 - 2x2 + 3x
H. 5x 3 + 10x 2 - 5x
Short Response
7. Suppose you have been given this polynomial.
5b + 4b2 - 3b4 + 3
a. How can you write this polynomial in standard form?
b. What is the degree of this polynomial? Explain.
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I. 5x 3 + 5x2 - x
Name Class Date Standardized Test Prep
Multiplying and Factoring
Multiple Choice
For Exercises 1–5, choose the correct letter.
1. How can this product be simplified?
A. 5x 2
5x2(2x - 3)
B. 10x 3 - 15x 2
+ 2x - 3
C. -5x2
D. 7x 3 - 15x 2
2. What is the GCF of the terms of 8c3 + 12c2 + 10c?
G. 4
F. 2
H. 2c
I. 4c
3. How can the polynomial 6d 4 + 9d 3 - 12d 2 be factored?
A. 3d 2(2d 2 + 3d - 4)
B. 3d 2(3d 2 + 6d - 9)
C. 3d(d 3 + 3d 2 - 4)
D. 6d 2(d 2 + 3d 3 - 6)
4. There is a circular garden in the middle of a square yard. The radius of the circle is 4x.
The side length of the yard is 20x. What is the area of the part of the yard that is not
covered by the circle?
G. 8x 2(5 - p)
F. 4x(5)
H. 16x(25 + p)
I. 16x 2(25 - p)
5. What is the simplified form of -3z 2(z + 2) - 4(z 2 + 1)?
A. -7z 2 + 1
B. -3z 3 - 4z 2 - 6z - 4
C. -3z 3 - 2z 2 - 4
D. -3z 3 - 10z 2 - 4
Short Response
6. A rectangular blacktop with a length of 5x and a width of 3x has been erected
inside a rectangular field that has a length of 12x and a width of 7x.
a. What is the area of the part of the field that is not blacktop?
b. There is a circular fountain in the rectangular field that has a radius of 3x.
What is the area of the part of the field that does not include the blacktop or
the fountain? Factor your answer.
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