Math Models B

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?

What is the factorization of 81a6 - 100?

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?

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?

Which is a factor of 144 − 49x2?

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?

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

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

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?

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?

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?

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

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

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

Which expression is equivalent to 64 − 9x2?

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

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

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

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

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

What is the square root of r64?

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

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

Which polynomial can be simplified to a difference of squares?

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

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

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

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

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

Which expression is equivalent to 100n2 - 1?

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

Which product is equivalent to 25x2 - 16?

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?

Which monomials are perfect squares? Check all that apply.

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 + )

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.

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

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

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

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