Exam 5: The Greatest Common Factor and Factoring by Grouping

Factor the expression as the sum or difference of two cubes.

Factor the polynomial by grouping the terms together two at a time.

Factor the expression as the sum or difference of two cubes.

Factor the expression completely. Look first for the greatest common factor.

Factor the polynomial completely; that is, once you are finished factoring, none of the factors you obtain should be factorable. If the polynomial is prime , so indicate.

One number is 2 times another. Their product is 2 times their sum. Find the numbers.

Solve the equation.

Factor the following problem completely. First, factor out the greatest common factor, and then factor the remaining trinomial.

I have a piece of cardboard that is twice as long as it is wide. If I cut a 1-inch by 1-inch square from each corner and fold up the resulting flaps, I get a box with a volume of 112 cubic inches. What are the dimensions of the cardboard?

Factor.

A company that manufactures typewriter ribbons knows that the number of ribbons it can sell each week, x , is related to the price p per ribbon by the equation . At what price should the company sell the ribbons if it wants the weekly revenue to be ? ( Hint : The equation for revenue is .)

Factor the trinomial.

Factor the trinomial.

Factor the trinomial.

Factor.

A company that manufactures typewriter ribbons knows that the number of ribbons it can sell each week, x , is related to the price p per ribbon by the equation . At what price should the company sell the ribbons if it wants the weekly revenue to be $4,000? ( Hint : The equation for revenue is .)

Solve the equation.

Factor the trinomial.

Factor the trinomial.

Factor.