Answers Summer 2026 Common Core Algebra I - MA3109 B-IC MEF22QXVIntroduction to Polynomials

Chapter 7 Unit TEST: Polynomial Equations and Factoring Answers

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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)

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

(2x)2 = 4x2

(2x2)2 = 4x4

(4x)2 = 8x2

(4x2)2 = 8x8

The variables X, Y, and Z represent polynomials where X = a, Y = 3a – 5, and Z = a2 + 2. What is X2Y – Z in simplest form?

2a2 – 5a – 2

3a3 – 6a2 – 2

–3a3 – 2

–3a2 – 2

The area of a rectangle is found by multiplying the base times the height. A rectangle with an area represented by 12x2 + 6x – 8 has a height of 4x.What is the base of the rectangle?

3x + –

3x2 + –

3x + –

3x + –

Armando used algebra tiles to represent the product .

He used the algebra tiles correctly.

He did not represent the two original factors correctly.

The signs on some of the products are incorrect.

Some of the products do not show the correct powers of x.

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

4xy

4xy2

24xy

24xy2

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

A 2-column table with 2 rows. First column is labeled m with entries m squared, 4 m. Second column is labeled negative 6 with entries negative 6 m, 16. First row is labeled m with entries m squared, negative 6 m. Second row is labeled 4 with entries 4 m, 16.

A 2-column table with 2 rows. First column is labeled m with entries m squared, 2 m. Second column is labeled negative 8 with entries negative 8 m, 16. First row is labeled m with entries m squared, negative 8 m. Second row is labeled 2 with entries 2 m, 16.

A 2-column table with 2 rows. First column is labeled m with entries m squared, negative 6 m. Second column is labeled negative 4 with entries negative 4 m, 16. First row is labeled m with entries m squared, negative 4 m. Second row is labeled negative 6 with entries negative 6 m, 16.

A 2-column table with 2 rows. First column is labeled m with entries m squared, negative 8 m. Second column is labeled negative 2 with entries negative 2 m, 16. First row is labeled m with entries m squared, negative 2 m. Second row is labeled negative 8 with entries negative 8 m, 16.

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

(x − 4)(x − 9)

(x − 3)(x − 12)

(x + 4)(x + 9)

(x + 3)(x + 12)

What is the factorization of 81a6 - 100?

(9a2 − 10)(9a3 + 10)

(9a2 − 10)(9a3 − 10)

(9a3 − 10)(9a3 + 10)

(9a3 − 10)(9a3 − 10)

The area of a square can be represented by the expression x10. Which monomial represents a side of the square?

x20

x100

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

Which statement is true about the polynomial –10m4n3 + 8m2n6 + 3m4n3 – 2m2n6 – 6m2n6 after it has been fully simplified?

It is a monomial with a degree of 4.

It is a monomial with a degree of 7.

It is a binomial with a degree of 6.

It is a binomial with a degree of 8.

Which expression is equivalent to 64 − 9x2?

(32)2 − (3x)2

(32)2 + (−3x)2

(8)2 − (3x)2

(8)2 + (−3x)2

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 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).

Which terms could be used as the last term of the expression below to create a polynomial written in standard form? Select three options.–5x2y4 + 9x3y3 +

–4x4y5

6x4y

–xy5

–

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Chapter 7 Unit TEST: Polynomial Equations and Factoring Answers

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