Question

Factor each trinomial below. Please show your work and check your answer. (1 point each)

x2 – 8x + 15
a2 – a – 20
a2 – 5a – 20
a2 + 12ab + 27b2
2a2 + 30a + 100

Answer 1

do you know how to factor?

Answer 2

Hint: factors of b that add up to c

Answer 3

x^2-8x+15
look at the last number
it is 15
can you name the factors or 15
1 times 15
anymore?

Answer 4

3 and 5... but 3+5 is not 8.. so what other factors do you need?

Answer 5

Yes, 3+5 DOES equal 8 :)

Answer 6

Ok let us know when you would like to learn the process, meanwhile I leave this to someone else to finish

Answer 7

okay sorry i was doing something

Answer 8

that's ok, someone else will come help

Answer 9

Ok, so when you multiply two binomials (e.g. X+3), it takes the form of:
\[(X+a)(X+b)\]where a,b are numbers and X is a variable. If you multiply that out, you get:
\[X^{2}+bX+aX+a*b = X^{2}+(a+b)X + (a*b)\]
So if you match this up with the first equation you get:
\[X^{2}-8X+15\]
-8 = a+b

15=a*b

Possible factors of 15:
1*15=15
-1*-15=15
3*5=15
-3*-5=15
Since -3*-5=15, and -3+(-5)=-8, you know that they are a and b.

Place them back into the original factor, solve for X, and you're done!
\[(X+a)(X+b)\]

Answer 10

now you can do all of the rest, good job Wired explaining it

Answer 11

TYVM :) Almost went with (aX+b)(cX+d), but that's more complicated. Best to start with the basics :)

Answer 12

yes always start with the basics