Question

How do you factor the expression $27+36x$?

Answer 1

Hint: We first explain the process of factorisation which is available for $27+36x$. We find the GCD of 27 and 36 to take it as common from the constants. We form the equation $27+36x$ as the multiplication of a constant and linear equation.

Complete step by step answer:
The given equation $27+36x$ is a linear equation of $x$.
We need to factorise the equation.
The only process that is available for this equation to factorise is to take a common constant out of the terms 27 and $36x$.
Now we are actually taking the constant from 27 and 36. We are finding the maximum possible constant to take out. It will be the greatest common divisor of the numbers 27 and 36.
Now, we need to find the GCD of 27 and 36.
$\begin{align}
  & 3\left| \!{\underline {\,
  27,36 \,}} \right. \\
 & 3\left| \!{\underline {\,
  9,12 \,}} \right. \\
 & 1\left| \!{\underline {\,
  3,4 \,}} \right. \\
\end{align}$
Therefore, the GCD will be $3\times 3=9$.
We are taking 9 as common from the numbers 27 and $36x$.
If we take 9 from 27, the remaining number will be $\dfrac{27}{9}=3$.
If we take 9 from $36x$, the remaining number will be $\dfrac{36x}{9}=4x$.
Now the common term 9 will form the multiplication of two terms. One being 9 and the other being the addition of 3 with $4x$.
Therefore, the factorisation is $27+36x=9\left( 3+4x \right)$.

Note:
We can verify the result of the factorisation by taking an arbitrary value of x where $x=2$.
We put $x=2$ on the left-hand side of the equation $27+36x$ and get
$27+36x=27+36\times 2=27+72=99$
Now we put $x=2$ on the right-hand side of the equation $9\left( 3+4x \right)$ and get
$9\left( 3+4x \right)=9\left( 3+4\times 2 \right)=9\times 11=99$.
Thus, verified the factorisation $27+36x=9\left( 3+4x \right)$.