Question

How do you factor $ 8x+16 $ ?

Answer 1

Hint:
 We will look at the definition of factorization. We will find a common factor for both the terms in the given expression. Then we will take the common factor and multiply it with an expression that results in the given expression. Our goal is to rewrite the given expression as a product of factors instead of the addition of terms as given in the question.

Complete step by step answer:
We define factorization as splitting a number or an expression as a product of smaller numbers or expressions, which are called as factors. The given expression is $ 8x+16 $ . This expression has two terms, $ 8x $ and $ 16 $ . Now, we have to find a common factor for both these terms. We can write $ 8x $ as $ 8x=8\times x $ . Similarly, we can split the number $ 16 $ as $ 16=8\times 2 $ . So, we can rewrite the given expression as the following,
 $ 8x+16=\left( 8\times x \right)+\left( 8\times 2 \right) $
From the above expression, we can see that 8 is a common factor for both terms. So, we can take 8 common and rewrite the expression as
 $ 8x+16=8\left( x+2 \right) $
So now, we have obtained the form of the expression as a product of factors. Therefore, we can factorize $ 8x+16 $ as $ 8\left( x+2 \right) $ .

Note:
 The concept of factorization is important while dealing with algebraic expressions. We have multiple algebraic identities that are used while factorizing an algebraic expression. We can factorize algebraic expressions of higher powers by using polynomial division. The polynomial division is also called the long division. There is also the method of synthetic division for dividing polynomials.