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
Show All Work
3
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.
so, you gonna show all your work, as instructed?
yes, i just need someone to check the answers, I really need this grade
bruh
To determine if anyone has done the Unit 3 sample work Lesson 8, you would need to check with your teacher or classmates. It is not possible for an AI bot like me to know the specific actions of individuals.
However, I can provide guidance on how to solve the problems in the lesson:
1. To find the sum or difference of 4x^7 and -6x^7, you simply combine the like terms. Since the two terms have the same variable and exponent, you can add or subtract the coefficients. In this case, 4x^7 - 6x^7 simplifies to -2x^7.
2. To write the polynomial 3 - 10x^2 - 7x + 3x^2 in standard form, you arrange the terms in descending order based on their exponents. The standard form of the polynomial can be written as -10x^2 + 3x^2 - 7x + 3. The polynomial has 4 terms and a degree of 2.
3. To find the polynomial that models the total number of common and Endler's guppies, you add the two given polynomials together. (3.2x^2 + 5x + 0.2) + (4.4x^2 - 5.1x + 1) simplifies to 7.6x^2 - 0.1x + 1.2.
4. To find the greatest common factor (GCF) of the terms in 4a^4 + 6a^2, you can factor out the common factors. In this case, the GCF is 2a^2.
5. To factor the expression 4x^3 + 8x^2 + 12x, you can factor out the greatest common factor, which is 4x. This gives you 4x(x^2 + 2x + 3).
6. The area of the remaining yard after the circular fountain is built can be found by subtracting the area of the fountain from the area of the yard. The area of the yard is given by the product of its dimensions, which are 10x and 15x. The area of the fountain can be calculated using the formula for the area of a circle with radius 4x, which is 16πx^2. Subtracting the area of the fountain from the area of the yard gives you 150x^2 - 16πx^2.
7. To simplify the product (2x - 5)(x + 3) using the distributive property, you multiply each term of the first polynomial by each term of the second polynomial. This gives you 2x^2 + 6x - 5x - 15, which simplifies to 2x^2 + x - 15.
For the remaining problems, the explanations would be similar to those provided above. Remember to show all your work and follow the given instructions for each question.