Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and -6 w2 - 7w - 6w - 42

Step-4 : Add up the first 2 terms, pulling out like factors : w • (w-7) Add up the last 2 terms, pulling out common factors : 6 • (w-7) Step-5 : Add up the four terms of step 4 : (w-6) • (w-7) Which is the desired factorization

Equation at the end of step 1 :

(w - 6) • (w - 7) = 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 : w-6 = 0

Add 6 to both sides of the equation : w = 6

Solving a Single Variable Equation :

2.3 Solve : w-7 = 0

Add 7 to both sides of the equation : w = 7

Supplement : Solving Quadratic Equation Directly

Solving w2-13w+42 = 0 directly Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula W=7,w=6