1.Choose the information that will make the statement correct.

To factor the expression 6x^3+3x^2+8x+4 by regrouping, split it into two groups: (6x^3+8x and 3x^2+4) or (6x^3+4 and 3x^2+8x) OR (4 and 6x^3+3x^2+8x) or (6x^3+3x^2 and 8x+4). The final result is x(6x^2+3x+8)+4 OR (3x^2+4)(2x+1) OR (x+2)(3x^2+8)

2.determine if each quotient has a remainder or no remainder.

(X+5)(X+2) / (x-2)(x+5)

X^2-1 / X-1

X^2+x+7/ X^2-x-12

(x-7)(x+4)(2x^2+1)(x^3-1)/ (2x^2+1)(x^2-3x-28)(x^2+x+1)(x-1)

3.A quotient is simplified by factoring and canceling common factors in the numerator and denominator.

A(x)=P1(x). P2(x)

------- ---------------

B(x) P3(x)

P1(x), P2(x) and P3(x) cannot be factored any further.

P3(x) does not equal B(x)

Select all that apply.

A-A(x) and B(x) have no common factors.

B-A(x) and B(x) have common factors

C-B(x) is a factor of A(x)

D- B(x) is not a factor of A(x)

E- P3(x) is not a factor of A(x)

F-P3(x) is not a factor of B(x)

4.Factor 27x^3+27x^2+9x+1 as completely as possible. If the factored expression is of the form (Ax+B)(Cx^2+Dx+E), answer the following questions.

What is A?

What is B?

What is C?

What is D?

What is E?

5.A trapezoid with bases of length x-2 units and x^2-x+3 units has an area of 1/2x^3- 3/2x^2+1/2x-3/2 units^2.Determine the height of the trapezoid in terms of x. Enter the height in standard form.

6.A rectangle has an area of 3m^2-21m+18in^2. What are the possible lengths and widths of the rectangle?Select all that apply.

A- 1 in and 3m^2-21m+18in

B-3in and m^2-7m+6 in

C-m-6 in and m-1 in

D-3m-18 in and m-1 in

E-m-6 in and 3m-3 in

7.F(x) represents a polynomial expression that can be factored to: A(x) . B(x) . C(x) . D(x) where A(x), B(x), C(x) and D(x) are polynomial expressions. If A(x) . B(x). C(x). D(x) represents the most complete factorization, then A(x), B(x), C(x) and D(x) must be linear polynomials OR A(x) must be the GCF OR A(x), B(x), C(x) and D(x) are polynomials with only two factors: 1 and itself. OR A(x), B(x), C(x), and D(x) are binomial expressions.

If F(x)=a^5b-ab^5, then ....

A(x)=ab OR a^4 b^4

B(x)=a-b OR a^2-b^2

C(x)=a+b OR a^4-b^4

D(x)=a^2+b^2 OR 1

8.Simplify the following rational expression.

a^3+b^3/ a+b

A.a^2+ab+b^2

B. a^2-ab+b^2

C. a^2

D. a^2+b^2

9.Eli claims that x^2-4/x-2 simplifies to x+2. His work is shown below:

X^2-4

-------- = X^2/ x + -4/-2 =X+2

x-2

Choose the correct information below to make each statement correct.

Eli correctly divided the dividend by the divisor OR did not correctly divide the numerator by the denominator. and should have factored the numerator and canceled the common factors in the numerator and denominator OR simplified his answer . X+2 is the Correct OR incorrect answer.

10.A juice box is made in the shape of a rectangular prism with a volume of 16x^4+8x^3+250x+125 cm^3.The side lengths are polynomials with integer coefficients. Deterime the side lengths of the juice box. Select all that apply.

A- 2x+1

B- 2x+5

c- 2x-5

D- 4x^2+10x+25

E- 4x^2-10x+25

F-8x^3+125