How do you factor the expression #x^2 - 12x + 36 #?

2 Answers
Mar 3, 2018

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.

Mar 3, 2018

#(x-6)^2#

Explanation:

#color(blue)((1))x^2-color(red)(12x)+36=x^2-color(red)(6x-6x)+36#
#=color(red)(x)(x-6)-color(red)(6)(x-6)#
#=(x-6)(x-6)#
#=(x-6)^2#
OR,Using #color(red)(A^2-2AB+B^2=(A-B)^2)#
We get,
#x^2-12x+36=(x)^2-2(x)(6)+(6)^2=(x-6)^2#