Answers FL-1200310-Algebra 1Adding and Subtracting Polynomials

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The model represents the factorization of 2x2+5x+3.

(2x+3)(x+1)

(2x−3)(x−1)

(3x+2)(x+1)

(3x−2)(x−1)

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Which is true about the completely simplified difference of the polynomials 6x6 − x3y4 − 5xy5 and 4x5y + 2x3y4 + 5xy5?

The difference has 3 terms and a degree of 6.

The difference has 4 terms and a degree of 6.

The difference has 3 terms and a degree of 7.

The difference has 4 terms and a degree of 7.

Which expression is equivalent to 64 − 9x2?

(32)2 − (3x)2

(32)2 + (−3x)2

(8)2 − (3x)2

(8)2 + (−3x)2

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?

4m(75m2 + 30m +40)

10m(30m2 + 12m +18)

30(10m2 +4m + 60)

60(5m2 +2m +3)

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

Profit is the difference between revenue and cost. The revenue, in dollars, of a company that makes skateboards can be modeled by the polynomial 2x3 + 30x – 130. The cost, in dollars, of producing the skateboards can be modeled by 2x3 – 3x – 520. The variable x represents the number of skateboards sold.

27x – 650

27x + 390

33x – 650

33x + 390

Which is a factor of 144 − 49x2?

12 - 7x2

72 – 7x2

12 – 7x

72 + 7x

What is the product?

2 x squared minus 3

2 x squared + 6 x

2 x squared + 5 x minus 3

2 x squared + 6 x minus 3

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)

Mrs. Ishimitsu is installing a rubber bumper around the edge of her coffee table. The dimensions of the rectangular table are (2x2 – 16) feet and (–x2 + 4x + 1) feet. Which expression represents the total perimeter of the table, and if x = 3, what is the length of the entire rubber bumper?

x2 + 4x – 15; 3 feet

x2 + 4x – 15; 6 feet

2x2 + 8x – 30; 6 feet

2x2 + 8x – 30; 12 feet

What is the product?(5r − 4)(r2 − 6r + 4)

5r3 − 34r2 + 44r − 16

5r3 − 4r2 + 14r − 16

5r3 − 6r − 16

5r3 + 10r − 16

Arpitha factors out the greatest common factor, 9n, from the terms of the polynomial shown.162m3n4 + 45n= 9n(_______ + 5)

16m3n3

16m3n4

18m3n3

18m3n4

What is the polynomial 3y2 + (y + 7)2 – 15 after it has been fully simplified and written in standard form?

4y2 + 34

3y2 + y + 34

4y2 + 14y + 34

4y4 + 34

What is the difference of the two polynomials?(7y2 + 6xy) – (–2xy + 3)

7y2 + 4xy – 3

7y2 + 8xy – 3

7y2 + 4xy + 3

7y2 + 8xy + 3

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

What is the product?

negative 81 t squared minus 16

negative 81 t squared + 16

negative 81 t squared minus 72 t + 16

negative 81 t squared + 72 t + 16

What is the product?

negative 81 t squared minus 16

negative 81 t squared + 16

negative 81 t squared minus 72 t + 16

negative 81 t squared + 72 t + 16

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 + x5y5–4x4y56x4y–xy5–

–4x4y5

6x4y

–xy5

–

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

x20

x100

27x – 650

27x + 390

33x – 650

33x + 390

What is the product?(5r − 4)(r2 − 6r + 4)

5r3 − 34r2 + 44r − 16

5r3 − 4r2 + 14r − 16

5r3 − 6r − 16

5r3 + 10r − 16

Which statement is true about the polynomial –3x4y3 + 8xy5 – 3 + 18x3y4 – 3xy5 after it has been fully simplified?

It has 3 terms and a degree of 5.

It has 3 terms and a degree of 7.

It has 4 terms and a degree of 5.

It has 4 terms and a degree of 7.

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.

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

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.

Sari is factoring the polynomial 2x2+5x+3. If one factor is (x+1), what is the other factor?

2x−3

2x+3

3x−2

3x+2

What is the greatest common factor of 8m, 36m3, and 12?

Four students are verifying thatx2 + x– 12 = (x – 3)(x + 4). Their conclusions are presented in the table.Which student correctly verified that x2 + x – 12 = (x – 3)(x + 4)?

Damien

Lauryn

Rico

Latisha

Which is true about the polynomial y2 – 3y + 12?

It is a binomial with a degree of 2.

It is a binomial with a degree of 3.

It is a trinomial with a degree of 2.

It is a trinomial with a degree of 3.

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

–

What is the factorization of 81a6 - 100?

(9a2 − 10)(9a3 + 10)

(9a2 − 10)(9a3 − 10)

(9a3 − 10)(9a3 + 10)

(9a3 − 10)(9a3 − 10)

What is the polynomial 3y2 + (y + 7)2 – 15 after it has been fully simplified and written in standard form?

4y2 + 34

3y2 + y + 34

4y2 + 14y + 34

4y4 + 34

Which is equivalent to , and what type of special product is it?

; a perfect square trinomial

; the difference of squares

; a perfect square trinomial

; the difference of squares

Rodney models the factorization of a trinomial with algebra tiles as shown.

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

4xy

4xy2

24xy

24xy2

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)

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.

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

Which is true about the completely simplified difference of the polynomials 6x6 − x3y4 − 5xy5 and 4x5y + 2x3y4 + 5xy5?

The difference has 3 terms and a degree of 6.

The difference has 4 terms and a degree of 6.

The difference has 3 terms and a degree of 7.

The difference has 4 terms and a degree of 7.

Mandisa draws a rectangle to represent the area of her yard. The area can be represented by 10x2 – 13x – 14.

(2x + 2) and (5x – 7)

(5x – 2) and (2x + 7)

(x – 2) and (10x + 7)

(10x + 2) and (x – 7)

Which is true about the polynomial y2 – 3y + 12?

It is a binomial with a degree of 2.

It is a binomial with a degree of 3.

It is a trinomial with a degree of 2.

It is a trinomial with a degree of 3.

Which is equivalent to , and what type of special product is it?

; a perfect square trinomial

; the difference of squares

; a perfect square trinomial

; the difference of squares

Which statement is true about the polynomial –3x4y3 + 8xy5 – 3 + 18x3y4 – 3xy5 after it has been fully simplified?

It has 3 terms and a degree of 5.

It has 3 terms and a degree of 7.

It has 4 terms and a degree of 5.

It has 4 terms and a degree of 7.

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.

x2 + 4x – 15; 3 feet

x2 + 4x – 15; 6 feet

2x2 + 8x – 30; 6 feet

2x2 + 8x – 30; 12 feet

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