Question

Factorize$5x + 35$.

Answer 1

Hint:The process Factorization simply means breaking a term or a polynomial into many smaller terms which upon multiplication yields the polynomial terms. Here we can perform factorization by taking the common terms outside if there are any, such that correspondingly the factors of this polynomial can be found.

Complete step by step solution:
Given
\[5x + 35.............................\left( i \right)\]

Normally the process factorization is done by:
1. Making a perfect square

2. Grouping terms by taking common factors within them.

3. Simply taking common factors if there are any.

So on inspecting $5x + 35$we observe that we cannot perform factorization by using the methods
described in 1 or 2 since it’s not compatible with those processes.

But also in $5x + 35$we observe that the number $5$is a common factor for both$5\;and\;35$.

So for factoring \[5x + 35\]we can use the process described in the 3 rd point.
i.e. taking common factors from the terms in (i):
$ \Rightarrow 5x + 35 = 5\left( {x + 7} \right)$

Since here the term $5$is common to both we take $5$from both the terms, also now there are no
common terms and thus we can stop the process.

Also on observing $5\left( {x + 7} \right)$we see that when $5$is multiplied inside the bracket we get the parent polynomial term.

Therefore on factoring $5x + 35$we get$5\left( {x + 7} \right)$.

Note:
While approaching a question one should study it properly and accordingly should choose the method to factorize the polynomial. Similar questions which cannot be expressed as perfect squares or cannot be grouped together should be approached using the same method as described above. Polynomial factorization is always done over some set of numbers which may be integers, real numbers or complex numbers.