Algebra GCF Unit Test Review, Math Models B, The Fundamental Theorem of Algebra, Addition and Subtraction of Polynomials

Which expression is equivalent to 100n2 - 1?

(10n)2 - (1)2

The model represents a perfect square monomial. What equation is represented by the model?

(2x)2 = 4x2

Factor -7x3 + 21x2 + 3x - 9 by grouping. What is the resulting expression?

(3 - 7x2)(x - 3)

Jenna constructs the model to represent 3x2 + 11x - 4. What factors does Jenna need to model for the sides?

(3x - 1) • (x + 4)

What is the factorization of 3x2 - 8x + 5?

(3x - 5) • (x - 1)

Which expression can be used to find the difference of the polynomials (4m - 5) - (6m - 7 + 2n)

(4m - 5) + (-6m + 7 - 2n)

Which product is equivalent to 25x2 - 16?

(5x - 4)(5x + 4)

Which expression is equivalent to 64 − 9x2?

(8)2 − (3x)2

Which expression is equivalent to 64 − 9x2? (32)2 − (3x)2 (32)2 + (−3x)2 (8)2 − (3x)2 (8)2 + (−3x)2

(8)2 − (3x)2

What is the factorization of 81a6 - 100?

(9a3 − 10)(9a3 + 10)

What is the factored form of the polynomial? x2 + 9x +20

(x + 4)(x + 5)

Mandisa draws a rectangle to represent the area of her yard. The area can be represented by 10x2 - 13x - 14. What expressions can Mandisa use to represent the length and width of her yard?

(x - 2) and (10x + 7)

What is the factored form of the polynomial? x2 − 15x + 36

(x − 3)(x − 12)

What is the factored form of x2 − 4x − 5?

(x − 5)(x + 1)

Which shows the four-term polynomial and factored form of x2 + 6x - 27?

(x+9)(x-3)

What is the factored form of x2 - x - 2?

(x-2)(x+1)

The binomial (y − 2) is a factor of y2 − 10y + 16. What is the other factor?

(y − 8)

What is the factored form of the polynomial? z2 − 10z + 25 (z − 5)(z − 5) (z + 5)(z + 5) (z − 2)(z + 5) (z + 2)(z − 5)

(z − 5)(z − 5)

10x3 + 3x2 - 20x - 6 (10x3 + 3x2) + (-20x - 6) x2(10x + 3) + (_______)(10x + 3) Teresa is factoring this polynomial by grouping. Which number goes in the blank to complete the step?

-2

What is the sum of the polynomials? 11x^2 - 5 + x + 4 ____________

11x^2 + x - 1

Which is a factor of 144 − 49x2?

12 - 7x

Which is a factor of 144 − 49x2? 12 - 7x2 72 - 7x2 12 - 7x 72 + 7x

12 - 7x

What is the greatest common factor of 60x4y7, 45x5y5, and 75x3y?

15x3y

Arpitha factors out the greatest common factor, 9n, from the terms of the polynomial shown. 162m3n4 + 45n = 9n(_______ + 5) What is the missing term in the factored expression?

18m3n3

Arpitha factors out the greatest common factor, 9n, from the terms of the polynomial shown. 162m3n4 + 45n = 9n(_______ + 5) What is the missing term in the factored expression? 16m3n3 16m3n4 18m3n3 18m3n4

18m3n3

Which polynomial can be simplified to a difference of squares?

25a2 + 6a - 6a + 36

Mrs. Ishimitsu is installing a rubber bumper around the edge of her coffee table. The dimensions of the rectangular table are (2x2 - 16) feet and (-x2 + 4x + 1) feet. Which expression represents the total perimeter of the table, and if x = 3, what is the length of the entire rubber bumper? x2 + 4x - 15; 3 feet x2 + 4x - 15; 6 feet 2x2 + 8x - 30; 6 feet 2x2 + 8x - 30; 12 feet

2x2 + 8x - 30; 12 feet

Which shows one way to determine the factors of 12x3 - 2x2 + 18x - 3 by grouping?

2x2(6x - 1) + 3(6x - 1)

Rodney models the factorization of a trinomial with algebra tiles as shown. Rodney forgot to place x-tiles in zero pairs in the model of the trinomial. How many zero pairs of x-tiles should he place in the model? pairs

3

Profit is the difference between revenue and cost. The revenue, in dollars, of a company that makes skateboards can be modeled by the polynomial 2x3 + 30x - 130. The cost, in dollars, of producing the skateboards can be modeled by 2x3 - 3x - 520. The variable x represents the number of skateboards sold. What expression represents the profit? 27x - 650 27x + 390 33x - 650 33x + 390

33x + 390

The diagram represents 6x2 - 7x + 2 with a factor of 2x - 1. What is the other factor of 6x2 - 7x + 2?

3x - 2

What is the sum of the polynomials? (6x + 7 + x^2) + (2x^2 - 3)

3x^2 + 6x + 4

The partial factorization of x2 - x - 12 is modeled with algebra tiles. Which unit tiles are needed to complete the factorization?

4 negative unit tiles

What is the fully factored form of 32a3 + 12a2?

4a2(8a + 3)

What is the sum of the polynomials? 17m - 12n - 1 + 4 - 13m - 12n ____________________

4m - 24n +3

Which polynomial has factors of 4x - 7 and x + 4?

4x2 + 9x - 28

Which polynomial has factors of 4x - 7 and x + 4? 3x2 + x - 3 4x2 + 9x - 28 3x2 - 7x - 3 4x2 - 23x - 28

4x2 + 9x - 28

What is the greatest common factor of 4xy2 and 20x2y4?

4xy2

Which terms could have a greatest common factor of 5m2n2? Check all that apply.

5m4n3 15m2n2

Paul creates the diagram to help him factor 4x2 + x - 5 by using double grouping. His diagram is incomplete. Which terms should Paul write in squares M1 and M2?

5x and −4x

The diagram represents the factorization of a2 + 8a + 12. What is the missing number that will complete the factorization? a2 + 8a + 12 = (a + 2)(a + )

6

Logan saves the same amount of money each month for college. His current total savings is 300m2 + 120m + 180 dollars. Which factorization could represent the number of months and amount of a monthly deposit in dollars?

60(5m2 +2m +3)

Logan saves the same amount of money each month for college. His current total savings is 300m2 + 120m + 180 dollars. Which factorization could represent the number of months and amount of a monthly deposit in dollars? 4m(75m2 + 30m +40) 10m(30m2 + 12m +18) 30(10m2 +4m + 60) 60(5m2 +2m +3)

60(5m2 +2m +3)

The polynomial 24x3 − 54x2 + 44x − 99 is factored by grouping. 24x3 − 54x2 + 44x − 99 24x3 + 44x − 54x2 − 99 4x(____) − 9(____) What is the common factor that is missing from both sets of parentheses?

6x2 + 11

The polynomial 24x3 − 54x2 + 44x − 99 is factored by grouping. 24x3 − 54x2 + 44x − 99 24x3 + 44x − 54x2 − 99 4x(____) − 9(____) What is the common factor that is missing from both sets of parentheses? 6x + 11 6x − 11 6x2 + 11 6x2 − 11

6x2 + 11

Which is the completely factored form of 18x4 - 42x3 + 24x2? 3x(3x - 4)(2x - 2) 3x2(3x - 4)(2x - 2) 6x(3x - 4)(x - 1) 6x2(3x - 4)(x - 1)

6x2(3x - 4)(x - 1)

What is the difference of the two polynomials? (7y2 + 6xy) - (-2xy + 3) 7y2 + 4xy - 3 7y2 + 8xy - 3 7y2 + 4xy + 3 7y2 + 8xy + 3

7y2 + 8xy - 3

What is the addictive inverse of the polynomial? -7^2 + x^2y - 3xy - 7x^2

7y^2 - x^2y + 3xy + 7x^2

Samuel found the difference of the polynomials. (15x^2 + 11y^2 + 8x) - (7x^2 + 5y^2 + 2x) = ____x^2 + 6y^2 + 6x What value is missing from his solution?

8

Which monomials are perfect squares? Check all that apply.

9x8 25x12 36x16

What is the sum of thy polynomials? (8x2^2 - 9y^2 - 4x) + (x^2 - 3y^2 - 7x)

9x^2 - 12y^2 - 11x

Which diagram represents the factors of m2 - 10m + 16 ?

Graph 4

Marcus finds that (3x^2 - 2y^2 + 5x) + (4x^2 + 12y^2 - 7x) = 7x^2 - 10y^2 - 2x. What error did Marcus make?

He combined the terms -2y^2 and 12y^2 incorrectly.

Marisol grouped the terms and factored the GCF out of the groups of the polynomial 6x3 - 22x2 - 9x + 33. Her work is shown. Step 1: (6x3 - 22x2) - (9x + 33) Step 2: 2x2(3x - 11) - 3(3x + 11) Marisol noticed that she does not have a common factor. Which accurately describes what Marisol should do next? Marisol should realize that her work shows that the polynomial is prime. Marisol should go back and group the terms in Step 1 as (6x3 - 22x2) - (9x - 33). Marisol should go back and group the terms in Step 1 as (6x3 - 22x2) + (9x - 33). Marisol should refactor the expression in Step 2 as 2x2(3x + 11) - 3(3x + 11).

Marisol should go back and group the terms in Step 1 as (6x3 - 22x2) - (9x - 33).

Omar grouped the terms and factored the GCF out of the groups of the polynomial 3x3 - 15x2 - 4x + 20. His work is shown. Step 1: (3x3 - 15x2) + (-4x + 20) Step 2: 3x2(x - 5) + 4(-x + 5) Omar noticed that he does not have a common factor. Which accurately describes what Omar should do next?

Omar should factor out a negative from one of the groups so the binomials will be the same.

Which is true about the completely simplified difference of the polynomials 6x6 − x3y4 − 5xy5 and 4x5y + 2x3y4 + 5xy5? The difference has 3 terms and a degree of 6. The difference has 4 terms and a degree of 6. The difference has 3 terms and a degree of 7. The difference has 4 terms and a degree of 7.

The difference has 4 terms and a degree of 7.

Which expression can be used to find the sum of the polynomials? (9 - 3x^2) + (-8x^2 + 4x + 5)

[(-3x^2) + (-8x^2)] + 4x + [9 + 5]

If 9i is a root of the polynomial function f(x), which of the following must also be a root of f(x)?

a. -9i

If f(x) is a third degree polynomial function, how many distinct complex roots are possible?

a. 0 or 2

How many x intercepts appear on the graph of this polynomial function? f(x)= x^4 - x^3 + x^2 - x

b. 2 x intercepts

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function? (9x + 7)(4x + 1)(3x + 4) = 0

b. 3 roots

Which of the following statements must be true about the polynomial function f(x)?

b. If 1 + 13i is a root of f(x), then 1 - 13i is also a root of f(x).

According to the Fundamental Theorem of Algebra, which polynomial function has exactly 11 roots?

b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

Two roots of a third degree polynomial function f(x) are -4 and 4. Which statement describes the number and nature of all roots for this function?

b. f(x) has three real roots.

The diagram represents the area of a rectangle as 9x2 + 24x + 16 square units. What are the length and width of the rectangle in terms of x?

both: 3x + 4 units

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function? f(x) = 8x^7 - x^5 + x^3 + 6

c. 7 roots

Which of the following describes the roots of the polynomial function f(x) = (x - 3)^4 (x + 6)^2?

d. 3 with multiplicity 4 and -6 with multiplicity 2

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function? f(x) = 4x^5 - 3x

d. 5 roots

Patricia is studying a polynomial function f(x). Three given roots of f(x) are -11-√2i, 3 + 4i, and 10. Patricia concludes that f(x) must be a polynomial with degree 4. Which statement is true?

d. Patricia is not correct because both 3 - 4i and -11+√2i must be roots.

According to the Fundamental Theorem of Algebra, which polynomial function has exactly 6 roots?

d. f(x) = 7x^6 + 3x^3 + 12

According to the Fundamental Theorem of Algebra, which polynomial function has exactly 8 roots?

fx = (3x^2 - 4x -5)(2x^6 - 5)

A rectangle has an area of (x2 − 17x + 72) square units. Since the area of a rectangle is determined using the formula, A = lw, what could be the length and width of the rectangle? length = (x − 8) units and width = (x − 9) units length = (x + 9) units and width = (x + 8) units length = (x − 6) units and width = (x − 12) units length = (x + 12) units and width = (x + 6) units

length = (x − 8) units and width = (x − 9) units

What is the difference of the polynomials? (m^2 n^2 - 7) - (mn + 4)

m^2 n^2 - mn - 11

What is the square root of r64?

r32

The factorization of a trinomial is modeled with algebra tiles. Which trinomial is factored?

x2 + x - 6

Which polynomials, given in square inches, could represent the area of a square with whole number side lengths if x is a whole number greater than 2? Remember, the formula for the area of a square is A = s2. Check all that apply.

x2 − 4x + 4 x2 + 10x + 25

Which shows one way to determine the factors of x3 + 11x2 - 3x - 33 by grouping?

x2(x+11)-3(x+11)

Which shows one way to determine the factors of x3 + 4x2 + 5x + 20 by grouping?

x2(x+4)+5(x+4)