Last time, we learned how to factor with tiles. Let’s take a quick review.

You are given a rectangular array of tiles. It represents a polynomial.

Determine the binomial factors of the polynomial.

Enter the values of the binomial factors into the text boxes. Then click the “Submit” button.

Now, let’s continue with today’s lesson.

A quadratic trinomial is a second degree polynomial with three terms.

Sometimes, it can be factored into the product of two binomials. For exmaple: <EQUATION>

In this lesson we are interested in quadratic trinomials of the form: <EQUATION>.

The <EQUATION> term has only a coefficient of <EQUATION>.

Here we have a quadratic trinomial of this form: <EQUATION>

Factoring it by trial and error would be tedious. Let’s learn a method that can help us out.

First, we want to find two numbers m and n...

Such that m + n equals the coefficient of the middle term...

In this example, the coefficient is 7.

The product <EQUATION> must also equal the number-only term.

In this example, the number is 10.

Now, what are m and n in this example? Click the “Submit” button after selecting your answer.

We see that 5 and 2 satisfy the conditions for m and n.

We add each of these to x to form our two binomial factors: (x + 5)(x + 2).

We can check the result by using the FOIL method. The product of the binomials is the original trinomial.

Now, try some examples on your own.

You are given a trinomial. Find its binomial factors.

After entering the values into the text boxes, click the “Submit” button.

Let’s apply what we learned to a problem. The surface area of a rectangular swimming pool is given by the equation: <EQUATION>

First, we rewrite the equation so that we have 0 on one side and a quadratic trinomial on the other side.

Next, we want to factor the trinomial into the product of two binomials.

Which of the following is the factored form of the trinomial? Click the “Submit” button after selecting your answer.

Now, we have two binomial terms equal to zero: (x + 9)(x – 4) = 0.

One of the binomials must equal 0.

What are the two possible values of x? Click the “Submit” button after selecting your answer.

We set each binomial factor equal to 0 and solve for x. The possible solutions are -9 and 4.

Because we are measuring something, only a positive value makes sense.

Copyright 2006 The Regents of the University of California and Monterey Institute for Technology and Education