Major Factoring Help?!?

Question

I have need to know the steps it takes to factor the following questions FULLY:

1. Factor Fully:

a) 4t^2-28t+40

b) x^3-4x^2+4x

c) 3y^2-27

Factor:

a) 4m^2+20m+25

b) 3t^2+8t+5

c)5r^s-11rs+2s^2

d) 121a^2-b^2

PLEASE SHOW AND EXPLAIN ALL STEPS AS I DO NOT KNOW HOW TO COMPLETE THESE TYPES OF QUESTIONS AT ALL.

Answer 1

for the first set.

you will need to factor out something then expand the bi-nomial.

a: factor out (4) since all three terms are divisible by "4"

so you have (4) (t^2 - 7t + 10) now lets factor the second term

(t - ?) (t - ?) to find what the ? is we need to look at the "10"

we need find factors of "+10" that when added or subtracted from each other we get "-7"

which means that (-5) and (-2) will be the answer

so we have: (4) (t - 2) (t - 5)

b. we first factor out an "x" to give us (x) (x^2 - 4x + 4) using the steps above solve this

c. factor out "3" to get  (3) (y^2 - 9)

the second tern you should recongize as a difference of two squares

good luck.