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# Factoring Trinomials

## Factoring a Trinomial of the Form x2+ bx+ c

To factor a trinomial of the form x2 + bx + c, we can use the product-sum method.

Procedure â€” To Factor x2+ bx+ c Using the Product-Sum Method

Step 1 Find two integers whose product is c and whose sum is b.

Step 2 Substitute the integers from Step 1 for the constants, r and s, in the binomial factors (x + r) and (x + s).

Example 1

Factor: x2 - 2x - 24

Solution

The trinomial x2 - 2x - 24 has the form x2 + bx + c where b = -2, and c = -24.

Step 1 Find two integers whose product is c and whose sum is b.

We seek two integers whose product is -24 and whose sum is -2.

Since the product, c = -24, is negative, the integers must have opposite signs.

Since the sum, b = 2, is negative, the integer with the greater absolute value must be negative.

Here are some possibilities:

 Product -24 Â· 1 -12 Â· 2 -8 Â· 3 -6 Â· 4 Sum -23 -10 -5 -2

The integers -6 and 4 give the required product, -24, and the required sum, -2.

Step 2 Substitute the integers from Step 1 for the constants, r and s, in the binomial factors (x + r) and (x + s).

The factorization is (x - 6)(x + 4).

You can multiply to check the factorization.

Note:

We can use FOIL to check the factorization:

 (x - 6)(x + 4) = x2 + 4x - 6x - 24= x2 - 2x - 24

The factorization checks.