Final answer:
To factor the expression 2c²+4c-84, first find the GCF (which is 2), then factor the trinomial inside the parentheses.
Step-by-step explanation:
To factor the expression 2c²+4c-84, we first need to find the greatest common factor (GCF) of the terms. In this case, the GCF is 2. So we can start by factoring out the GCF:
2c²+4c-84 = 2(c²+2c-42)
Next, we need to factor the trinomial inside the parentheses. To do this, we look for two numbers whose product is -42 and whose sum is 2. The numbers 7 and -6 meet these conditions, so we can rewrite the expression as:
2(c+7)(c-6)
Therefore, the expression 2c²+4c-84 factors completely to 2(c+7)(c-6).