Introduction to Factoring Polynomials: example 10.84

Factor: $2 x + 14 .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Factor: $4 x + 12 .$

How did it go?

Step 1: Find the GCF of all the terms of the polynomial.	Find the GCF of 2x and 14.
Step 2: Rewrite each term as a product using the GCF.	Rewrite 2x and 14 as products of their GCF, 2. $2 x = 2 \cdot x$ $14 = 2 \cdot 7$
Step 3: Use the Distributive Property 'in reverse' to factor the expression.		$2 (x + 7)$
Step 4: Check by multiplying the factors.		Check:

Step 1: Find the GCF of all the terms of the polynomial.	Find the GCF of 2x and 14.
Step 2: Rewrite each term as a product using the GCF.	Rewrite 2x and 14 as products of their GCF, 2. $2 x = 2 \cdot x$ $14 = 2 \cdot 7$
Step 3: Use the Distributive Property 'in reverse' to factor the expression.		$2 (x + 7)$
Step 4: Check by multiplying the factors.		Check: