What are some examples, and non-examples of factoring?

Question

johnweldon1993 · Answer

umm okay...say we have

x² +8x + 16

how do we factor that? first we find the factors of 16

16,1
8,2
4,4

....now...which one of these groupings add to get 8? ...well 4 and 4 right?

so we have

(x + 4)(x + 4)

also can be written as (x+4)²

to check ..we can multiply it out

(x + 4)(x + 4)

what is x times x? x²
what is x times 4? 4x
what is 4 times x? 4x
what is 4 times 4? 16

put what we have

x² + 4x + 4x + 16

***********4x + 4x = 8x*************

so we have

x² + 8x + 16

not sure how clear that is but...

anonymous · Answer

Thank you! that does help

johnweldon1993 · Answer

okay good :) also....if you dont want to factor you can use the quadratic formula..which i will now write

johnweldon1993 · Answer

$$-b \pm \sqrt{b ^{2}-4ac}/2a$$

where a is your coefficient of x²..which is 1
b is your coefficient of 8x....which is 8
c is your coefficient of 16....which is 16

plug those numbers in...go through the whole equation...and you would come out with

$$-8 \pm \sqrt{8^{2}-4(1)(16)} / 2(1)$$

what is 8²? 64
what is 4 times 1 times 16? 64

so we have

$$-8 \pm \sqrt{0}/2$$

square root of 0? is 0

so your final answer would be -8/2...or -4,-4

how do we turn those -4's into 0?
add 4
so

(x+4)(x+4)


same thing.. but stick to factoring for now :)

anonymous · Answer

You are awesome at math! thanks for the help!:)

johnweldon1993 · Answer

lol...it'll become second nature to you as well eventually :) just practice practice practice :)
and like i told you before...anytime :)