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.
3 answers
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