Factoring Quadratic Trinomials

We continued factoring polynomials today, but we kept them to the form ax² + bx + c. These are called quadratic polynomials because of the ax² term.

Example: Factor x² + 5x - 36

1. Consider factors of the constant term (c, or the last term). Here: -36 is -1*36; -2*18; -3*12; -4*9; -6*6; -9*4; -12*3; -18*2; -36*1.


2. Choose the pair of factors whose sum is the coefficient of the linear term (b, or the middle term). Here: -4 + 9 = 5


3. Create your factors (2 sets of parenthesis) by filling in the variable and the factors chosen in step 2. Here: (x - 4) (x + 9)

For our Hopewell Middle School students, we made the link from today's lesson to the Diamond Puzzles that they did several times last year. They were presented with a diamond with two numbers. They were instructed to find two numbers that multiply to make the upper number and add to make the lower number. The following diamond puzzle is similar to the above example.

The two numbers needed to complete the puzzle are -9 and 4, as shown below.

Homework: Page 83: #1 - 9; Page 84: #1 - 6; Page 91: #1, 7, and 13

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