Question

Find the quotient when $9{x^2} - 45x$ is divided by $9x$.

Answer 1

Hint: The given problem requires us to find the quotient in the division of two given numbers. So, in order to find the quotient, we first write the expression in fraction form and then simplify. We factor out the common terms in the numerator and then cancel out the common factors in numerator and denominator to get to the required answer.

Complete step by step answer:
In the given question, we are required to find the quotient when $9{x^2} - 45x$ is divided by $9x$. So, we write the given information in fraction form. So, we get,
$ \Rightarrow \dfrac{{9{x^2} - 45x}}{{9x}}$
Now, we will simplify the fractional expression. So, we first factor out the common factors from both the terms in the numerator and take them outside of the bracket. We notice that both the terms $9{x^2}$ and $45x$ have $9x$ as the common factor.

So, taking $9x$ out of the bracket by factorization, we get,
So, we get,
$ \Rightarrow \dfrac{{9x\left( {x - 5} \right)}}{{9x}}$
Now, we will cancel the common factors in the numerator and denominator of the fractional expression in x. We notice that the common factor in the numerator and denominator of $\dfrac{{9x\left( {x - 5} \right)}}{{9x}}$ is $9x$. So, cancelling $9x$ , we get,
$ \Rightarrow \dfrac{{\left( {x - 5} \right)}}{1}$
Since the denominator is one. So, we can write the expression simply as,
$ \therefore \left( {x - 5} \right)$

Hence, the quotient obtained on dividing $9{x^2} - 45x$ by $9x$ is $\left( {x - 5} \right)$.

Note: Quadratic polynomials are the polynomials with degree of the variable or unknown as $2$. Quadratic polynomials can be simplified by factoring common factors and taking them out of the bracket. We must cancel the common factors in the numerator and denominator of a fraction to simplify the expression. We should have a good grip over the simplification rules to tackle these problems.