# has anyone done the Unit 3 sample work lesson 8?

3-1 Adding and Subtracting Polynomials (pg.474)

1. What is the sum or difference?

4x^7 − 6x^7

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

3 − 10x^2 − 7x + 3x^2

3. 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: 3.2x^2 + 5x + 0.2

Endler’s guppies: 4.4x^2 − 5.1x + 1

What polynomial models the total number of common and Endler’s guppies?

3-2 Multiplying and Factoring Polynomials (pg.480)

4. What is the GCF of the terms in 4a^4 + 6a^2?

5. Factor.

4x^3 + 8x^2 + 12x

6. A family is building a circular fountain in the backyard. The yard is rectangular and measures 10x by 15x and

the fountain is going to be circular with a radius of 4x. Once the fountain is built, what will be the area of the

remaining yard?

3-3 Multiplying Binomials (pg.486)

7. Simplify the product using the distributive property

(2x − 5)(x + 3)

Algebra 1B

3-8 Sample Work

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8. Simplify using the table

(−3y + 2)(5y + 4)

-3y +2^5y^+4

9. Simplify the product using FOIL

(8x − 1)(6x − 7)

10. A cylinder has a radius of x + 2 and a height of x + 4. Which polynomial in standard form best describes the

total volume of the cylinder? Use the formula V = πr

2h for the volume of a cylinder.

11. A carpenter is putting a skylight on 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?

3-4 Multiplying Special Cases (pg.492)

12. Simplify.

(2r − 3)(2r + 3)

13. What is the simpler form of the product?

(3x − 5y^3)^2

3-5 Factoring x^2 + bx + c (pg.500)

14. Factor the expression.

x^2 + 7x + 12

Algebra 1B

3-8 Sample Work

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15. The area of a rectangular room is given by the trinomial x

2 + 3x − 40. What are the possible dimensions of

the rectangle? Use factoring.

16. What is the factored form of the following expression?

x^2 + 12xy + 32y^2

3-6 Factoring ax^2 + bx + c (pg.506)

17. Factor the expression.

3x^2 + 16x + 5

18. The area of a rectangular picture frame is given by the trinomial 6x

2 − 11x − 72. What are the possible

dimensions of the frame? Use factoring.

3-7 Factoring Special Cases (pg.511)

19. What is the factored form of the expression?

w^2 + 18w + 81

20. What is the factored form of the expression?

t^2 − 144

21. f(x) = 11x^3 + 3x^2 − 4x + 2 and g(x) = 5x

3 − 7x + 2. What is f(x) − g(x)? Show all of your steps and

write your final answer in factored form.