STEP 1 : Trying to factor by splitting the middle term
1.1 Factoring q2-4q-12
The first term is, q2 its coefficient is 1 . The middle term is, -4q its coefficient is -4 . The last term, "the constant", is -12
Step-1 : Multiply the coefficient of the first term by the constant 1 • -12 = -12
Step-2 : Find two factors of -12 whose sum equals the coefficient of the middle term, which is -4 .
-12 + 1 = -11 -6 + 2 = -4 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and 2 q2 - 6q + 2q - 12
Step-4 : Add up the first 2 terms, pulling out like factors : q • (q-6) Add up the last 2 terms, pulling out common factors : 2 • (q-6) Step-5 : Add up the four terms of step 4 : (q+2) • (q-6) Which is the desired factorization
Equation at the end of step 1 :
(q + 2) • (q - 6) = 0 STEP 2 : Theory - Roots of a product
2.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation:
2.2 Solve : q+2 = 0
Subtract 2 from both sides of the equation : q = -2
