Factor the polynomial is a very effective tool which is utilized in the factorization. In polynomial, poly means many so this tool can e used for any type, that is, it can be used to factorize monomial, binomial, trinomial or higher etc. This tool uses step by step instructions to factorize and also it is used to factorize by adapting all factorization rules and methods. The most important point here is to understand the applicability of formula to be used in different-different problems.
Question 1:- Factor the following expression: - x^2 + 14x+ 49
Solution 1:- In this question given expression is x^2+ 14x + 49
This is basically a quadratic equation, so here we will us middle term splitting method, which is shown below
That is: - x^2 + 7x + 7x + 49
= x(x+7) +7 (x+7)
= (x+7) (x+7)
So this is the required equation.
Question 2:- Factor the following expression: - x^3 + 50x^2 + 50x+2500
Solution 2:- In this question given expression is x^3 + 50x^2 + 50x + 2500
There is basically no common factor in above equation for all four terms. But it is quite clear that there is some common factor between first and second term and also between third and fourth term. So we will take common accordingly
Therefore x^3 + 50x^2 + 50x + 2500
= x^2 (x+ 50) + 50(x+50)
Now we can see that (x+50) can be taken out
So x^3 + 50x^2 + 50x + 2500= (x+50) (x^2 +50)