1st Quarter Review in Math 8

Consider the polynomial expression 6x3 + 9x2. What is the common monomial factor of this polynomial?

• 3x

• 6x2

• 3x2

• x3

Look at the following expression: 4x2-9. Which of the following represents the factored form of this difference of two squares?

• (2x+3) (2x-3)

• (4x+3) (x-9)

• (x+3) (x-3)

• (2x+9) (2x-9)

The polynomial 12x3+18x2+6x is shown. How would you explain the process of factoring this polynomial?

• Factor out the common monomial factor 6x2.

• Factor out the common monomial factor 6x, then divide each term by 6x.

• Rewrite the polynomial as a product of two binomials.

• Combine all terms to create a perfect square trinomial.

The expression x2+10x+25 is provided. How can you interpret this polynomial to identify its factored form?

• Since the middle term is twice the square root of the first and third terms, it is a perfect square trinomial, factored as (x+5)2.

• Factor it as (x+10) (x+25) because the signs are all positive.

• This is a sum of squares that can't be factored.

• Recognize it as a general trinomial and apply the AC method for factoring.

Consider the expression 9x2-49. Apply the difference of squares formula to factor this expression. What is the correct factorization?

• (3x-7) (3x+7)

• (9x-7) (x+49)

• (x-7) (x+9)

• (3x+49) 3x-9)

The trinomial x2+12x+36 is shown. Using the perfect square trinomial factoring method, apply the appropriate technique to factor the expression. What is the factored form?

• (x+6) (x+6)

• (x+12) (x+3)

• (x-6) (x+6)

• (x+36) (x-1)

Examine the expression 6x2+13x+6. Which of the following analysis methods would you use to factor this general trinomial?

• Factor by grouping after splitting the middle term into two terms that multiply (6X6=36) and add to 13.

• This is a perfect square trinomial, so factor as (3x+2)2.

• It is a difference of squares, so factor it as (6x+6) (x-1).

• Apply the sum of cubes formula since both terms are cubed.

Consider the expression 16x2-36. Which analysis of the expression explains the correct factorization?

• It is a perfect square trinomial, so it should be factored as (4x-6)2.

• It is a general trinomial, so it should be factored as (4x-6) (4x+6).

• It is a difference of squares, so it factors as (4x-6) (4x+6).

• There is no factorization possible since both terms are perfect squares but not a difference of squares.

A teacher provides the trinomial x2+10x+21 and the possible factorizations: (x+7) (x+3), (x+1) (x+21), (x-7) (x-3). Evaluate the factorizations. Which option correctly factors the trinomial?

• Only option 1 is correct.

• Both options 1 and 2 are correct.

• Only option 2 is correct.

• None of the options are correct.

Consider the rational expression 3x/x2+5x. What is the correct classification of this expression?

• A polynomial

• A rational algebraic expression

• A linear equation

• A quadratic equation