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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) |
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What is the factorization of 81a6 – 100? |
(9a3 − 10)(9a3 + 10) |
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Omar grouped the terms and factored the GCF out of the groups of the polynomial 3×3 – 15×2 – 4x + 20. His work is shown. Step 1: (3×3 – 15×2) + (-4x + 20) Step 2: 3×2(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. |
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Mandisa draws a rectangle to represent the area of her yard. The area can be represented by 10×2 – 13x – 14. What expressions can Mandisa use to represent the length and width of her yard? |
(x – 2) and (10x + 7) |
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Which is a factor of 144 − 49×2? |
12 – 7x |
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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 |
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What is the factored form of the polynomial? x2 − 15x + 36 |
(x − 3)(x − 12) |
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Which polynomial has factors of 4x – 7 and x + 4? |
4×2 + 9x – 28 |
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The diagram represents the area of a rectangle as 9×2 + 24x + 16 square units. What are the length and width of the rectangle in terms of x? |
both: 3x + 4 units |
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10×3 + 3×2 – 20x – 6 (10×3 + 3×2) + (-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 |
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The polynomial 24×3 − 54×2 + 44x − 99 is factored by grouping. 24×3 − 54×2 + 44x − 99 24×3 + 44x − 54×2 − 99 4x(____) − 9(____) What is the common factor that is missing from both sets of parentheses? |
6×2 + 11 |
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The model represents a perfect square monomial. What equation is represented by the model? |
(2x)2 = 4×2 |
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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 |
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What is the greatest common factor of 4xy2 and 20x2y4? |
4xy2 |
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Which expression is equivalent to 64 − 9×2? |
(8)2 − (3x)2 |
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Factor -7×3 + 21×2 + 3x – 9 by grouping. What is the resulting expression? |
(3 – 7×2)(x – 3) |
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The factorization of a trinomial is modeled with algebra tiles. Which trinomial is factored? |
x2 + x – 6 |
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The diagram represents 6×2 – 7x + 2 with a factor of 2x – 1. What is the other factor of 6×2 – 7x + 2? |
3x – 2 |
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Which terms could have a greatest common factor of 5m2n2? Check all that apply. |
5m4n3 15m2n2 |
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What is the greatest common factor of 60x4y7, 45x5y5, and 75x3y? |
15x3y |
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What is the square root of r64? |
r32 |
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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 |
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Which shows one way to determine the factors of 12×3 – 2×2 + 18x – 3 by grouping? |
2×2(6x – 1) + 3(6x – 1) |
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Which polynomial can be simplified to a difference of squares? |
25a2 + 6a – 6a + 36 |
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Which shows one way to determine the factors of x3 + 4×2 + 5x + 20 by grouping? |
x2(x+4)+5(x+4) |
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What is the factored form of x2 − 4x − 5? |
(x − 5)(x + 1) |
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Which shows the four-term polynomial and factored form of x2 + 6x – 27? |
(x+9)(x-3) |
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What is the factored form of the polynomial? x2 + 9x +20 |
(x + 4)(x + 5) |
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What is the factorization of 3×2 – 8x + 5? |
(3x – 5) • (x – 1) |
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Which expression is equivalent to 100n2 – 1? |
(10n)2 – (1)2 |
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What is the fully factored form of 32a3 + 12a2? |
4a2(8a + 3) |
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Which product is equivalent to 25×2 – 16? |
(5x – 4)(5x + 4) |
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Paul creates the diagram to help him factor 4×2 + x – 5 by using double grouping. His diagram is incomplete. Which terms should Paul write in squares M1 and M2? |
5x and −4x |
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Which monomials are perfect squares? Check all that apply. |
9×8 25×12 36×16 |
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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 |
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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 |
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Jenna constructs the model to represent 3×2 + 11x – 4. What factors does Jenna need to model for the sides? |
(3x – 1) • (x + 4) |
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Which shows one way to determine the factors of x3 + 11×2 – 3x – 33 by grouping? |
x2(x+11)-3(x+11) |
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What is the factored form of x2 – x – 2? |
(x-2)(x+1) |
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The binomial (y − 2) is a factor of y2 − 10y + 16. What is the other factor? |
(y − 8) |
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