# Factor x^2+bx+c - Rahway Public Schools Factor Factoring a Quadratic Trinomial Factoring quadratics of the form (when the coefficient of is 1) Ex: =10 =7 1+10=11 2+5=7 Step 1: Set up your binomials. +2 +5 2 and 5 are the factors of 10 that add up to 7 Step 2: Insert the two numbers that have a product of c and a sum of b. Step 3: Check your solution by multiplying out the binomials! (+ 2)( +5)

2+5 +2 +10 2+7 +10 Watch Your Signs! The signs of your c and b values are VERY important! Example: Factor c=8 =6 9 1 8=8 1 (8)=81+ ( 8 ) =9 6 2 ( 4)=8 * When your product (c) is positive and your sum (b) is negative, you will need two negative factors. ( 2 )( 4) Check:

Will you ever be able to add two positive numbers and get - 6? You Try: Factor 2 7 +12=( 4)( 3) Keep Watching Your Signs! The signs of your c and b values are still VERY important! ( 3 )( +8 ) Example: Factor c=24 =5 1( 24)=24 1 ( 24 )=24 2 (12 ) =24 3 ( 8 ) =24

1+ ( 24 ) =23 Check: 1+24=23 2+12=10 3 +8=5 * When your product (c) is negative and your sum (b) is positive, the smaller factor will be negative and the larger factor will be positive. We want a positive result, so we need to keep the larger factor positive. You Try: Factor 2 + 56=( 7)( + 8)

Signs, Signs, Signs. The signs of your c and b values are still VERY important! ( +3 )( 8 ) Example: Factor c=24 =5 1( 24)=24 1 ( 24 )=24 2 ( 12 ) =24 3 ( 8 ) =24 1+ ( 24 ) =23 Check: 1+24=23 2+ ( 12 )=10 3+ ( 8 ) =5

* When your product (c) is negative and your sum (b) is negative, the smaller factor will be positive and the larger factor will be negative. We want a negative result, so we need to keep the larger factor negative. You Try: Factor 2 +3 18=( +6)( 3) Practice Factor: 3) 4) 1)