Question

Factorise the following algebraic expression,
                   ${{y}^{4}}-2{{y}^{3}}+y-2$

Answer 1

Hint: In the above question we will have to know about the factorisation. Factorisation is the process of finding what to multiply together to get the given expression . It is like “splitting” an expression into a multiplication of simpler expressions. In the given expression we will take common and we will use the formula to factorize it more further and by using the formula we can easily get the result, the formula is shown below,
\[{{a}^{3}}+{{b}^{3}}=(a+b)({{a}^{2}}-ab+{{b}^{2}})\]

Complete step-by-step answer:

Now for the given algebraic expression the factorising is as follow,
\[\begin{align}
  & \Rightarrow {{y}^{4}}-2{{y}^{3}}+y-2={{y}^{3}}(y-2)+y-2 \\
 & \Rightarrow ({{y}^{3}}+1)(y-2) \\
 & \Rightarrow (y+1)({{y}^{2}}-y+1)(y-2) \\
\end{align}\]
Hence, it is factorised into the factors as shown above.

Note: Just remember the formula and be careful while doing calculation because there is a chance that you might make silly mistakes and thus you will get the incorrect answer. Also remember all the algebraic formulae because it will help you a lot in these types of questions. In case if you do not get common factors for the pairs formed, try rearranging the terms and follow the same procedure again. Also once go through the factor theorem and remainder theorem for the polynomial because it will be very helpful in the questions related with it.