Algebra 1 Semester 2 Unit Test Review

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 noticed that she does not have a common factor. Which accurately describes what Marisol should do next? 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).

B

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

B

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.

B

Teresa is factoring this polynomial by grouping. Which common factors should be used in the next step of factoring? 10x3+3x2−20x−6 (10x3+3x2)+(−20x−6) x2 and −2x 2x2 and −2x x2 and −2 2x2 and −2

C

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? 6x + 11 6x − 11 6x2 + 11 6x2 − 11

C

The volume of a rectangular prism can be found by multiplying the base area, B, times the height. If the volume of the prism is represented by 15x2 + x + 2 and the height is x2, which expression represents B, the area of the base? 15x + + 15x + + 15 + + 15 + +

C

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

C

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 + -

A

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)

A

What is the greatest common factor of 8m, 36m3, and 12? 4 8 4m 8m

A

What is the product? (5r − 4)(r2 − 6r + 4) 5r3 − 34r2 + 44r − 16 5r3 − 4r2 + 14r − 16 5r3 − 6r − 16 5r3 + 10r − 16

A

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 realize that his work shows that the polynomial is prime. Omar should go back and regroup the terms in Step 1 as (3x3 - 15x2) - (4x + 20). In Step 2, Omar should factor only out of the first expression. Omar should factor out a negative from one of the groups so the binomials will be the same.

D

The polynomial 8x2 - 8x + 2 - 5 + x is simplified to 8x2 - gx - h. What are the value of g and h? g = -9 and h = 7 g = 9 and h = -3 g = -7 and h = 7 g = 7 and h = 3

D

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.

D

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.

D