Math Models B
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)
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
The diagram represents 6x2 - 7x + 2 with a factor of 2x - 1. What is the other factor of 6x2 - 7x + 2?
3x - 2
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)
Which polynomial has factors of 4x - 7 and x + 4?
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
Which monomials are perfect squares? Check all that apply.
9x8 25x12 36x16
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 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)
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 product is equivalent to 25x2 - 16?
(5x - 4)(5x + 4)
Which expression is equivalent to 64 − 9x2?
(8)2 − (3x)2
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
Which is a factor of 144 − 49x2?
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
Which polynomial can be simplified to a difference of squares?
25a2 + 6a - 6a + 36
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)
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 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
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
