Question

How do you factor \[9p+12\]?

Answer 1

Hint: From the question given we have to find the factor of the \[9p+12\]. Firstly, the given polynomial contains two terms means it is a binomial. In the given polynomial first, we will take three common from both the terms and then we will equate it to zero. We will get the factor of the given polynomial.

Complete step by step solution:
From the question given polynomial is
\[\Rightarrow 9p+12\]
 By observing the polynomial, it contains two terms which means it is a binomial. As we know that any polynomial containing two terms is known as binomial.
Now, we have to find the factors of the given polynomial.
\[\Rightarrow 9p+12\]
For finding the factor first we will take three common from the both the terms in the polynomial.
By taking three common from the both the terms in the given expression we will get,
\[\Rightarrow 3\left( 3p+4 \right)\]
 Now, equate this expression with the zero then we will get the value of p.
By equating the above expression with zero we will get,
\[\Rightarrow 3\left( 3p+4 \right)=0\]
\[\Rightarrow \left( 3p+4 \right)=0\]
Now shift the 4 from the left hand side of the equation to the right-hand side.
By shifting the 4 from left hand side to the right-hand side of the equation we get,
\[\Rightarrow 3p=-4\]
Now, shift the 3 from the left hand side to the right-hand side of the equation.
By shifting the 4 from left hand side to the right-hand side of the equation we get,
\[\Rightarrow p=\dfrac{-4}{3}\]
Therefore, the factor of the \[9p+12\] is \[\left( p+\dfrac{4}{3} \right)\] or \[\left( 3p+4 \right)\].

Note:
Students should know the different types of polynomials like monomial, binomial, trinomial etc. monomial contains one term, binomial contains two terms, trinomial contains three terms.