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Algebra/common binomial factors

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Expert: - 2/6/2010


Question
okay so I understand this: (x + 2)x + (x+2)(10)
but this is what I'm having problems with:

PROBLEM: xsquared (5y-z) - (12x-20) (5y-z)
I GET: (5y-z) [xsquared - 1 (12x-20)]
THEN I GET: (5y-z) [(x-1) (x+1) (12x-20)]
AND THEN: (5y-z) [xsquared (12x-20)]

i know this is wrong because the answer in the back of the book says the answer is: (5y-z) (x+1) (x-4)

where did i go wrong?

Answer
Hello Lizzy,

I don't think the step where you went from:

(5y-z) [xsquared - 1 (12x-20)]

to:

(5y-z) [(x-1) (x+1) (12x-20)]

is correct.

First of all, let's use"x^2" instead of "xsquared" (that's the way you usually type powers BTW). Notice that you have

(5y-z) [x^2 - 1 (12x-20)]

WHICH IS DIFFERENT FROM (notice the parentheses):

(5y-z) [(x^2 - 1) (12x-20)]

So you can't do what you did on the third step because you don't have (x^2-1) in the first place, you have

(5y-z)[x^2 -(12x-20)] = (5y-z) [x^2 -12x+20],

so you have to factorize [x^2-12x+20]

Just so you know, I got

(5y-z)(x-10)(x-2)

which is also different from the answer you found at the back of the book. I think that answer is also wrong.

Cheers,
David  

Algebra

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