Question

how factorisation is done? Explain with some examples.

Answer 1

$\sf\textsf{How to Factorise the Quadratic equation ?}$

$\begin{array}{crclc}&&-252t^2&&\\&&\swarrow\searrow&&\\&18t&&-14t&\end{array}\quad\boxed{\begin{minipage}{6cm}\item\bigstar \quad \; \, t^2+4t-252=0 \\\begin{itemize} \item t^2\times(-252)\;\,=-252t^2 \item -252t^2\qquad\;\, = 18t\times-14t \item 18t+(-14t)\, =4t \end{itemize}\end{minipage}}$

$\mapsto \sf{t^2+18t-14t-252} = 0\\ \mapsto \sf{t(t+18t)-14(t+18)} = 0\\ \mapsto \sf{(t+18)(t-14)}=0\\\mapsto \sf{t-14} = 0\\\mapsto \sf{t=14}$

$\rule{200}{2}$

For factorising we have to follow the following steps :

1. Firstly, we will multiply the first and last term.
2. We will saw the product of both and would make two factors. Whose product is equal.
3. After that we will make factors of product, so that the sum or subtraction of the middle term is equal to the product of the thiemrd terms.