Question

Can anyone check my Math answers in Polynomials and factoring?

Answer 1

What is the sum or difference?
1. 3x8 – 7x8 (1 point)
–4x16
–21x8
–4x8
10x8
What is the sum or difference?
2. 10y10 – 14y10 (1 point)
–4y20
–140y20
–140y10
–4y10
3. Write the polynomial in standard form. Then name the polynomial based on its degree and number of terms.

6 – 12x + 13x2 – 4x2 (1 point)
9x2 – 12x; quadratic binomial
9x2 – 12x + 6; quadratic trinomial
–3x2 + 6; quadratic binomial
9x2 – 12x –6; cubic trinomial
4. A biologist studied the populations of common guppies and Endler’s guppies over a 6-year period. The biologist modeled the populations, in tens of thousands, with the following polynomials where x is time, in years.

common guppies: 3.1x2 + 6x + 0.3

Endler’s guppies: 4.2x2 – 5.2x + 1

What polynomial models the total number of common and Endler’s guppies? (1 point)
7.3x2 + 0.8x + 0.7
7.3x2 – 0.8x + 1.3
7.3x2 + 0.8x + 1.3
7.3x2 + 0.8x – 1.3
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 – 4pix2
42x2 – 2pix2
38pix2
6. A family is building a new house on a rectangular lot of land. The lot measures 7x by 11x and the house will be 2x by 3x. How much land will be left for their yard after the house is built? (1 point)
77x2
83x2
40x2
71x2
7. Simplify the product using the distributive property.

(4r –5)(7r + 2) (1 point)
28r2 + 43r – 10
28r2 – 27r + 10
28r2 + 43r + 10
28r2 – 27r – 10
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. Simplify using a table.

(–4m + 6)(3m + 2)
–4m 6
3m
2
(1 point)
–12m2 + 10m + 12
–12m2 – 10m – 12
–12m2 + 26m + 12
–12m2 – 26m – 12
10. Simplify the product using FOIL.

(3x – 4)(6x – 2) (1 point)
18x2 + 30x – 8
18x2 + 18x – 8
18x2 – 30x + 8
18x2 – 18x + 8
11. A cylinder has a radius of 5x + 2 and a height of 2x + 8. Which polynomial in standard form best describes the total volume of the cylinder? Use the formula V = pir2h for the volume of a cylinder. (1 point)
100pix4 + 880pix3 + 2256pix2 + 1408pix + 256pi
50pix3 + 240pix2 + 168pix + 32pi
20pix3 + 168pix2 + 384pix + 128pi
10pix2 + 44pix + 16pi
12. A sphere has a radius of 2x + 5. Which polynomial in standard form best describes the total surface area of the sphere? Use the formula S = 4pir2 for surface area of a sphere. (1 point)
16pix2 + 80pix + 100pi
16pix2 + 40pix + 100pi
100pix2 + 80pix + 16pi
100pix2 + 100pi
13. What is a simpler form of the product?

(3x – 7y4)2 (1 point)
9x2 – 21xy4 + 49y8
9x2 – 42xy4 + 49y8
9x2 – 42xy4 – 49y8
9x2 + 49y8
14. Factor.

3x3 + 15x2 – 2x – 10 (1 point)
(x + 5)(3x2 + 2)
(x – 5)(3x2 + 2)
(x – 5)(3x2 – 2)
(x + 5)(3x2 – 2)
15. The area of a rectangular room is given by the trinomial x2 + 4x – 12. What are the possible dimensions of the rectangle? Use factoring. (1 point)
(x – 6) and (x – 2)
(x + 6) and (x + 2)
(x – 6) and (x + 2)
(x + 6) and (x – 2)
16. The area of a rectangular garden is given by the trinomial x2 + x – 30. What are the possible dimensions of the rectangle? Use factoring. (1 point)
(x – 6) and (x – 5)
(x + 6) and (x – 5)
(x + 6) and (x + 5)
(x – 6) and (x + 5)
17. What is the factored form of the following expression?

x2 – 4xy – 21y2 (1 point)
(x + 3y)(x – 7y)
(x – 3y)(x – 7y)
(x + 3y)(x + 7y)
(x – 3y)(x + 7y)
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 picture frame is given by the trinomial 3x2 – 9x – 30. What are the possible dimensions of the frame? Use factoring. (1 point)
(3x + 6) and (x – 5)
(3x + 6) and (–x – 5)
(3x – 6) and (x – 5)
(3x – 6) and (x + 5)
20. A family is building a rectangular patio in their backyard. The rectangular yard has dimensions of (8x+2) by (6x + 3) and they are planning the patio to be (x + 5) by (3x + 1). What is the area of the remaining yard after the patio has been built? (1 point)
3x2 + 16x + 5
48x2 + 36x + 6
51x2 + 52x + 11
45x2 + 20x + 1
21. What is the factored form of the expression?

w2 + 16w + 64 (1 point)
(w + 8)(w – 8)
(w + 64)(w – 1)
(w + 8)2
(w – 8)2
What is the factored form of the expression?
22. d2 + 22d + 121 (1 point)
(d + 11)2
(d – 11)2
(d – 11)(d + 11)
(d – 121)(d – 1)
23. What is the factored form of the expression?

t2 – 81 (1 point)
(t + 9)(t – 9)
(t + 81)(t – 1)
(t + 9)2
(t – 9)2
24. A box has a volume given by the trinomial x3 + 4x2 – 5x. What are the possible dimensions of the box? Use factoring. (1 point)
x, x – 5, and x + 1
x, x + 5, and x – 1
x, x + 5, and x + 1
x, x – 5, and x – 1
25. A freezer has a volume given by the trinomial y3 – 2y2 – 35y. What are the possible dimensions of the box? Use factoring. (1 point)
y, y + 5, and y – 7
y, y – 5, and y – 7
y, y + 5, and y + 7
y, y – 5, and y + 7