Factoring a Trinomial with Leading Coefficient 1 · Physics Playground

Example 2 from Algebra and Trigonometry, 1.5 Factoring Polynomials

Factoring a Trinomial with Leading Coefficient 1

Factor $x^{2} + 2 x - 15.$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
We have a trinomial with leading coefficient $1, b = 2,$ and $c = −15.$ We need to find two numbers with a product of $−15$ and a sum of $2.$ In the table below, we list factors until we find a pair with the desired sum.

Factors of $−15$ Sum of Factors

$1, −15$ $−14$

$−1, 15$ 14

$3, −5$ $−2$

$−3, 5$ 2

Now that we have identified $p$ and $q$ as $−3$ and $5,$ write the factored form as $(x - 3) (x + 5) .$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Factor $x^{2} - 7 x + 6.$

How did it go?