Question

if a is the one factor of X, what is the other factor

Answer 1

If $\mathsf{a}$ is the one factor of $\mathsf{x}$, then the other factor is $\mathsf{\dfrac{x}{a}}$.

Concept to be used:

• If $\mathsf{f(x)}$ be any function with two factors $\mathsf{g(x)}$ and $\mathsf{h(x)}$, then

• $\underline{\mathsf{f(x)=g(x)\times h(x)}}$

Step-by-step explanation:

Given, $\mathsf{a}$ is the one factor of $\mathsf{x}$.

Let the other factor be $\mathsf{p}$.

Then, $\mathsf{x=a\times p}$

$\Rightarrow \mathsf{a\times p=x}$

$\Rightarrow \boxed{\mathsf{p=\dfrac{x}{a}}}$ [transposing $\mathsf{a}$ to the right hand side, where $\mathsf{a}$ is non-zero]

Another example:

We take a function: $\mathsf{f(x)=x^{2}+2x+1}$ and one factor $\mathsf{g(x)=x+1}$.

Then the other factor:

$\quad \mathsf{h(x)=\dfrac{f(x)}{g(x)}}$ [where $\mathsf{g(x)}$ is non-zero]

$\Rightarrow \mathsf{h(x)=\dfrac{x^{2}+2x+1}{x+1}}$

$\Rightarrow \boxed{\mathsf{h(x)=x+1}}$