Question

How do you factor $9x-36$?

Answer 1

Hint:We are given a one-degree polynomial equation. This can be solved by factoring it using the grouping method. We can factor it by analyzing the common factor of coefficient of x and the constant term. This common factor shall be then taken common from both the terms and then the left-over terms shall be dealt with and solved further.

Complete step-by-step answer:
We are given a simple one-degree polynomial equation where there are only two terms. One of them is the x-term with its coefficient and the other is a constant term. The coefficient of x is 9 and the constant term is 36.
On finding the factors of 9 and 36, we get that the greatest common factor of both of them is 9. This is because we know that $9\times 4=36$ and 9 is a factor of itself as well.
Thus, we shall take 9 common and group the remaining terms together.
We get $9\left( x-4 \right)$.
To further solve and find the value of x, we must equate the formed equation with zero.
  $\Rightarrow 9\left( x-4 \right)=0$
Since, 9 cannot be equal to 0, therefore, we get
$x-4=0$
$\Rightarrow x=4$
Hence, on factoring the given equation, we find that the value of x is equal to 4.
Also, on factoring $9x-36$, we transform it as $9\left( x-4 \right)$.

Note:
We shall also get much more complex quadratic or bi-quadratic or even higher degree polynomials to be factorized. In that case, one must be careful enough to find the right common factors of the multiple terms given. We must also be careful enough while grouping the terms in order to avoid mistakes.