Algebra GCF Unit Test Review

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 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)

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

12 - 7x

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

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

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

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

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? 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

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

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

Graph 4

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).

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.