Question

How do you factor $4x + 12$ ?

Answer 1

Hint: In this question, we are given an algebraic expression as it contains a combination of numerical values and alphabets. When the alphabet representing an unknown quantity is raised to some power, the expression is said to be a polynomial equation. In this question, the equation can be called a polynomial equation as x is raised to the power 1 that is a non-negative integer. Now, a polynomial equation has as many factors as the degree of the equation, the highest power of x in this equation is 1 so its degree is 1 and it has exactly 1 solution. For finding the factor of the above equation, we will put it equal to 0 and then solve it.

Complete step by step solution:
We have $4x + 12 = 0$
$
   \Rightarrow 4(x + 3) = 0 \\
   \Rightarrow x + 3 = 0 \\
   \Rightarrow x = - 3 \\
 $
Hence, the factor of the equation $4x + 12$ is $x + 3$.

Note: The solutions/roots/zeros of an equation are defined as those values of x at which the value of the equation comes out to be zero, that’s why we put the equation equal to zero. And the factor of an equation is another algebraic expression that completely divides the original equation. Instead of taking 4 common to find the factors, we can also try another method. We can simply take all the constant terms to one side such that the terms containing x remain on the other side. We can then find the value of x by performing the given arithmetic operation and get the correct answer.