question

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?

answer

60(5m2 +2m +3)

question

What is the factorization of 81a6 - 100?

answer

(9a3 β 10)(9a3 + 10)

question

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?

answer

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

question

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?

answer

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

question

Which is a factor of 144 β 49x2?

answer

12 - 7x

question

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?

answer

18m3n3

question

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

answer

(x β 3)(x β 12)

question

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

answer

4x2 + 9x - 28

question

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?

answer

both: 3x + 4 units

question

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?

answer

-2

question

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

answer

6x2 + 11

question

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

answer

(2x)2 = 4x2

question

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

answer

3

question

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

answer

4xy2

question

Which expression is equivalent to 64 β 9x2?

answer

(8)2 β (3x)2

question

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

answer

(3 - 7x2)(x - 3)

question

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

answer

x2 + x - 6

question

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

answer

3x - 2

question

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

answer

5m4n3
15m2n2

question

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

answer

15x3y

question

What is the square root of r64?

answer

r32

question

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

answer

4 negative unit tiles

question

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

answer

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

question

Which polynomial can be simplified to a difference of squares?

answer

25a2 + 6a - 6a + 36

question

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

answer

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

question

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

answer

(x β 5)(x + 1)

question

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

answer

(x+9)(x-3)

question

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

answer

(x + 4)(x + 5)

question

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

answer

(3x - 5) β’ (x - 1)

question

Which expression is equivalent to 100n2 - 1?

answer

(10n)2 - (1)2

question

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

answer

4a2(8a + 3)

question

Which product is equivalent to 25x2 - 16?

answer

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

question

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?

answer

5x and β4x

question

Which monomials are perfect squares? Check all that apply.

answer

9x8
25x12
36x16

question

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 + )

answer

6

question

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.

answer

x2 β 4x + 4
x2 + 10x + 25

question

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

answer

(3x - 1) β’ (x + 4)

question

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

answer

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

question

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

answer

(x-2)(x+1)

question

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

answer

(y β 8)