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Old 01-16-2008   #1
suave9
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Default A few basic factoring problems

I took a break for 2 semesters away from math and it has turned out to be a big mistake. I can't even remember basic factoring.

I need an explanation on how to solve these problems or if you don't have the time, just solve them for me and i'll figure them out:

Factor completely -

4w + 12 - zw - 3z

9r + 24t

2p(p is cubed) + 8p(p is squared) - 10p

t(squared) - 100

b(cubed) - 27

Solve:

z(squared) + 11z + 24 = 0

25x(x is squared) + 4 = 20x

Thanks
 
Old 01-21-2008   #2
favtbg
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4w + 12 - zw - 3z
--this one you can factor by grouping.
4w + 12 - (zw + 3z) = 4(w + 3) - z(w + 3) = (4 - z)(w + 3)

9r + 24t
--what is the Greatest Common Factor (GCF) of 9 and 24
answer: 3(3r + 8t)

2p(p is cubed) + 8p(p is squared) - 10p
--factor p and 2 first since each term has a p and a 2 in common
so you should have: 2p(p^2 + 4p - 5)
Afterward, factor the second expression
answer: 2p(p - 1)(p + 5)

t(squared) - 100
--this is an expression of Difference of Square
answer: (t - 10)(t + 10)

b(cubed) - 27
--this is an expression of Difference of Cube
answer: (b - 3)(b^2 + 3b + 9)

Solve:

z(squared) + 11z + 24 = 0
--find two factors of 24 that when you add them together you get 11
24 has factors of 8 and 3; 8 + 3 is 11
answer: (z + 8)(z + 3)=0
z = -8 or z = -3

25x(x is squared) + 4 = 20x
--bring 20x to one side so you have the equation equal to zero
25x^2 - 20x + 4 = 0
(5x - 2)(5x - 2) = 0
x = 2/5

Hope that helps!
Best regard
 
 

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