Question

Factorize: \[12x + 15\]

Answer 1

Hint:
Here, we will first express each term of the given expression as the product of two numbers. Then we will factor out common terms to get the required answer. Factorization is a process of rewriting the expression in terms of the product of the factors.

Complete step by step solution:
We are given with a linear expression \[12x + 15\].
We will rewrite each term as a product of 2 numbers. Therefore, we get
\[12x + 15 = 3 \times 4x + 3 \times 5\]
Here, we can see 3 is common between both the terms. So, factoring out the common term 3 , we get
\[ \Rightarrow 12x + 15 = 3\left( {4x + 5} \right)\]

Therefore, the factor of the linear equation \[12x + 15\] is \[3\left( {4x + 5} \right)\].

Additional Information:
The given expression is a linear polynomial. A polynomial is an expression that is a combination of both constants and variables of different degrees. A linear polynomial is defined as a polynomial which has the highest degree of variable as 1. A quadratic polynomial has the highest degree of 2 and similarly, a cubic polynomial has the highest degree of variable as 3.

Note:
We know that the process of converting the higher degree polynomial as the product of factors of its lower degree polynomial which cannot be factored further is called Factorization. Factors are numbers if the expression is a numeral. Factors are algebraic expressions if the expression is an algebraic expression. Factorization is done by using the common factors, the grouping of terms and the algebraic identity. When a polynomial has to be factored then we should remember that whatever be the method of factorization, we should take out the common factor at first.