Factoring Polynomials with the Distributive Property

What is the greatest common factor (GCF) that can be factored out from the polynomial 4x^3 + 20x^2 + 24x?

• 2x

• x

• 8x

• 4x

After factoring out the GCF from 4x^3 + 20x^2 + 24x, what type of polynomial remains?

• Quadratic

• Quartic

• Linear

• Cubic

Which method is used to factor the expression 14x^4 - 21x^2?

• Common factor

• Quadratic formula

• Grouping

• Sum and difference

What is the factored form of 9x^2 - 4 using the sum and difference formula?

• (3x - 2)(3x + 2)

• (3x - 4)(3x + 4)

• (9x - 2)(x + 2)

• (x - 2)(x + 2)

In the expression x^3 + 2x^2 + 3x + 6, what is the common factor for the first binomial group?

• x

• 3x

• 2x

• x^2

What is the result of factoring the polynomial x^3 - 2x^2 - 9x + 18 by grouping?

• (x - 2)(x^2 - 9)

• (x + 2)(x^2 - 9)

• (x - 3)(x^2 - 9)

• (x + 3)(x^2 - 9)

What are the dimensions of a box if the volume is 12 cubic inches, the width is one inch less than the length, and the height is four inches greater than the length?

• Length = 4 inches, Width = 3 inches, Height = 8 inches

• Length = 3 inches, Width = 2 inches, Height = 7 inches

• Length = 5 inches, Width = 4 inches, Height = 9 inches

• Length = 2 inches, Width = 1 inch, Height = 6 inches

What is the factored form of x^3 + 3x^2 - 4x - 12?

• (x + 2)(x + 2)(x - 3)

• (x - 2)(x + 2)(x - 3)

• (x - 2)(x - 2)(x + 3)

• (x + 2)(x - 2)(x + 3)

Which of the following is a correct step in solving the volume equation for the box?

• Applying the quadratic formula directly to the volume equation

• Using the distributive property to combine like terms

• Factoring the trinomial to simplify the equation

• Multiplying the binomials to eliminate parentheses

What is the correct method to solve for the dimensions of the box described in the problem?

• Applying the Pythagorean theorem

• Calculating the derivative

• Factoring the polynomial equation

• Using the quadratic formula