Exam 5: The Greatest Common Factor and Factoring by Grouping

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

If a rocket is fired vertically into the air with a speed of feet per second, its height at time t seconds is given by . Here is a graph of its height at various times, with the details left out. How long will the rocket be in the air? ( Hint : How high is it when it hits the ground?)

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

A company manufactures diskettes for home computers. It knows from experience that the number of diskettes it can sell each day, x , is related to the price p per diskette by the equation . At what price should the company sell the diskettes if it wants the daily revenue to be $5,400? ( Hint : The equation for revenue is .)

Solve the equation.

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

Factor.

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

Factor the expression by taking out the greatest common factor.

Factor the expression by taking out 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.

Factor.

Factor the expression by taking out the greatest common factor.

One number is 9 more than twice another. Their product is 26. Find the numbers.

Factor the trinomial.

The equation is already in factored form. Use the special zero factor property to set the factors to 0 and solve.

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.

The shorter leg of a right triangle is 3 yards. If the hypotenuse is 5 yards, how long is the other leg? __________ yards

Factor the trinomial.

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