Factor tree is a tool which is used to find out the factorization with the help of factorization methods. Like tree has many branches, in the similar way it is required to solve factorization problems in various steps. Tree basically resembles the factorization steps which generally step by step procedure. It not only factorizes the expression but it also helps in solving the equations.
Question 1:- Factor and solve the following expression: - x^2 + 14x+ 48= 0
Solution 1:- In this question given expression is x^2+ 14x + 48
This is basically a quadratic equation, so here we will us middle term splitting method, which is shown below
That is: - x^2 + 6x + 8x + 48
Therefore x(x+6) + 8(x+6) = 0
So (x+8) (x+6) = 0
From above equation we have seen that x = -8 and x = -6 is the required solution of the given equation.
Question 2:- Factor the following expression: - x^3+ 11 x^2 +11 x+ 121
Solution 2:- In this question given expression is x^3 + 11x^2 + 11 x + 121
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 + 11 x^2 + 11 x + 121
= x^2 (x+ 11) + 11 (x+11)
Now we can see that (x+11) can be taken out
So x^3 + 25x^2 + 25x + 625= (x+11) (x^2 +11)