Question

What is the sum or difference?
1. 3x8 – 7x8
(1 point)–4x16
–21x8
–4x8
10x8

2. 6y5 – 9y5
(1 point)–3y10
15y5
–54y5
–3y5

Write the polynomial in standard form. Then name the polynomial based on its degree and number of terms.


3. 2 – 11x2 – 8x + 6x2
(1 point)–5x2 – 8x + 2; quadratic trinomial
–5x2 – 8x; quadratic binomial
–6x2 – 8x – 2; cubic polynomial
6x2 – 8x + 2; cubic trinomial

Answer 1

4. 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.

White-sided jackrabbits: 5.5x2 – 9.2x + 6.9
Black-tailed jackrabbits: 5.5x2 + 9.9x + 1.3



What polynomial models the total number of white-sided and black-tailed jackrabbits?


(1 point)11x2 + 0.7x + 8.2
11x2 – 0.7x + 8.2
11x2 – 0.7x – 8.2
–11x2 + 0.7x – 8.2

5. A family is having a pool built in their backyard. If their yard is rectangular and measures 7x by 6x and the pool is circular with a radius of 2x how much of the yard will be left over after the pool is built?
(1 point)38x2
42x2 – 4x2
42x2 – 2x2
38x2

6. A sports team is building a new stadium on a rectangular lot of land. If the lot measures 6x by 10x and the sports field will be 1x by 4x, how much of the lot will be left over to build bleachers on?
(1 point)56x2
64x2
30x2
60x2

Simplify the product using the distributive property.

7. (5h – 3)(3h + 7) (1 point)15h2 – 44h + 21
15h2 – 26h – 21
15h2 + 44h + 21
15h2 + 26h – 21

Simplify the product using a table.
8. (5h + 4)(3h + 6)



3h
6

5h



4




(1 point)15h2 + 42h + 24
15h2 – 42h + 24
15h2 + 18h – 24
15h2 – 18h – 24

9. (–2h + 4)(5h + 7)


5h
7

–2h



4



(1 point)–10h2 + 34h – 28
–10h2 + 6h + 28
–10h2 – 6h + 28
–10h2 – 34h – 28

Simplify the product using FOIL.
10. (4x – 4)(3x – 4) (1 point)12x2 – 28x + 16
12x2 – 4x – 16
12x2 + 4x – 16
12x2 + 28x + 16

11. A cylinder has a radius of 4x + 2 and a height of 5x + 4. Which polynomial in standard form best describes the total volume of the cylinder? Use the formula V = r2h for the volume of a cylinder.
(1 point)80x3 + 144x2 + 84x + 16
80x3 – 144x2 + 84x + 16

80x3 + 144x2 + 84x – 16
80x3 + 144x2 – 84x + 16

12. A sphere has a radius of 4x + 4. Which polynomial in standard form best describes the total surface area of the sphere? Use the formula S = 4r2 for the surface area of a sphere.
(1 point)64x2 + 128x + 64
64x2 – 128x + 64
64x2 + 128x – 64
64x2 – 128x – 64

What is a simpler form of each product?

13. (4x – 6y3)2
(1 point)16x2 – 24xy3 + 36y6
16x2 – 48xy3 + 36y6
16x2 + 36y6
16x2 – 4xy3 + 36y6

14. Factor 5a3 + 15a2 – 6a – 18. (1 point)(a2 – 6)(5a + 3)
(5a2 – 3)(a + 6)
(5a2 – 6)(a + 3)
(a2 + 6)(5a – 3)

15. The area of a rectangular garden is given by the trinomial x2 + 6x – 27. What are the possible dimensions of the rectangle? Use factoring.
(1 point)x – 9 and x + 3
x + 9 and x – 3
x – 9 and x – 3
x + 9 and x + 3

16. The area of a rectangular painting is given by the trinomial x2 + 4x – 21. What are the possible dimensions of the painting? Use factoring.
(1 point)x + 7 and x + 3
x – 7 and x + 3
x – 7 and x – 3
x + 7 and x – 3

What is the factored form of the following expressions?

17. x2 – 10xy + 24y2
(1 point)(x + 6y)(x + 4y)
(x – 2y)(x + 12y)
(x + 2y)(x – 12y)
(x – 6y)(x – 4y)

18. The area of a rectangular barnyard is given by the trinomial 6x2 + 7x – 20. What are the possible dimensions of the barnyard? Use factoring.
(1 point)2x – 5 and 3x + 4
–2x + 5 and –3x + 4
2x + 5 and 3x – 4
2x – 5 and 3x – 4

19. The area of a rectangular pool is given by the trinomial 2y2 + y – 3. What are the possible dimensions of the pool? Use factoring.
(1 point)(–y – 1) and (–2y – 3)
(y – 1) and (2y + 3)
(2y – 1) and (2y + 3)
(2y + 1) and (y – 3)

20. A carpenter is putting a skylight in a roof. If the roof measures 10x + 9 by 7x + 7 and the skylight measures x + 5 by 3x + 3, what is the area of the remaining roof after the skylight is built?
(1 point)67x2 + 115x + 48
73x2 + 151x + 78
70x2 + 133x + 63
3x2 + 18x + 15

For questions 21–23, what is the factored form of the expression?

21. d2 + 18d + 81

(1 point)(d + 9)(d – 9)
(d + 9)2
(d – 81)(d – 1)
(d – 9)2

22. d2 + 22d + 121

(1 point)(d + 11)2
(d – 11)2
(d – 11)(d + 11)
(d – 121)(d – 1)

23. r2 – 49

(1 point)(r – 7)(r + 7)
(r + 7)(r + 7)
(r – 7)(r – 7)
(r – 7)(r + 9)

24. A box has a volume given by the trinomial x3 + 3x2 – 18x. What are the possible dimensions of the box? Use factoring.
(1 point)x – 3, –x – 3, and –x – 6
x, x + 3, and x – 6
x, x – 3, and x + 6
x – 6, x – 6, and x + 6

25. A refrigerator has a volume given by the trinomial y3 + y2 – 56y. What are the possible dimensions of the refrigerator? Use factoring.
(1 point)y, y + 8, and y – 7
y, y – 8, and y + 7
y + 7, y + 7, and y – 7
y + 8, –y + 8, and –y + 7