By using factorization algorithm, we can factor any given expression.
Explanation:
For quadratic polynomials, the algorithm is as follows:
First, multiply the coefficient of the highest degree term and the constant. In this case, it is (1).(36)=36
Now, check the factors of the product and find how many different ways they can be arranged to get the product.
36=1.36
=2.18
=4.9
=6.6
=12.3
Now, you have to choose the pair of factors in such a way that adding them or subtracting them must be equal to the middle term coefficient.
We choose 6.6 because -6-6=-12 which is the coefficient of the middle term.
Now, split the middle term as -6x-6x, since the factors we chose are -6 and -6.
That is,
x
2
-6x-6x+36.
Now, take out the common factors from each pair.
That is, x(x-6)-6(x-6)
Finally, (x-6)(x-6) is the required factored form.
