Question

x2 + 24x + 144
Part 1: Explain how the polynomial is factored.
Part 2: Provide the factors

Answer 1

Have you heard of the sum and product method? Or something similar in wording?

Answer 2

no

Answer 3

Well ok. It is basically like this:
x^2 is the 1st term
24x is the 2nd term
144 is the 3rd term
Do you understand this?

Answer 4

Now you have to look at the 3rd term (144). What two numbers multiply to get the 2nd term (24x)? (just forget about the x for the moment)

Answer 5

There are many possiblities:
12 * 12
24 * 6
72 * 2
etc
Which ones of these multiplication factors ADD to get the 2nd term?
eg 12+12=24
24+6= 24
72+2=24

Answer 6

Then you have the brackets (x + ?) (x +?)
When expanding you know that x * x =x^2. Now those two factors that are multiplied to get the 3rd term and are added to get the 2nd term, goes where the ? are.

Answer 7

so (x+12)(x+12). To double check you got it right, expand:
=x^2 +12x +12x +144
=x^2+24x+144
Therefore it is correct.