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 April 7th, 2010, 05:36 AM #1 Senior Member   Joined: Apr 2010 Posts: 128 Thanks: 0 I need help in factorising power of quad and 3 unknown I find myself two question unable to solve through my text books , it all involves factorization. It's a challenge from my mathematics teacher to my class.(in my middle and high school text book , there are no solutions for power quad nor 3 unknown) 1) Factorize . (x^2 + x)^2 - 8(x^2 + x) + 12 2) Factorize . abc - a^2b + ab^2 - a + b - c
April 7th, 2010, 12:22 PM   #2
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Re: I need help in factorising power of quad and 3 unknown

Hello, rnck!

Quote:
 $\text{1. Factor: }\;(x^2 \,+\, x)^2 \,-\, 8(x^2 \,+\, x) \,+\, 12$

$\text{Let: }\:u \:=\^2\,+\,x" />

$\text{Then we have: }\;u^2\,-\,8u\,+\,12 \;=\;(u\,-\,2)(u\,-\,6)$

$\text{Back-substitute: }\;(x^2\,+\,x\,-\,2)(x^2\,+\,x\,-\,6)$

$\text{Factor again: }\;(x\,-\,1)(x\,+\,2)(x\,-\,2)(x\,+\,3)$

 April 8th, 2010, 12:42 AM #3 Senior Member   Joined: Apr 2010 Posts: 128 Thanks: 0 Re: I need help in factorising power of quad and 3 unknown Thanks soroban....(I have forgotten substitution that my past year teacher thought) *It looks like....i've been tricked.....by my mathematics teacher....(i went as far as pascal triangle but resolve nothing)
April 8th, 2010, 12:54 AM   #4
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Re: I need help in factorising power of quad and 3 unknown

Quote:
 Originally Posted by rnck 2) Factorize . abc - a^2b + ab^2 - a + b - c
soroban , since the answer you provided is exactly same as my mathematics teacher's answer , i guess i can conclude all of his answers are correct.

Here's the answer for the quote above (ab-1) (a-b-c)

What missing is working step which i failed to even form one.....any formula / steps recommendation?

April 8th, 2010, 04:20 AM   #5
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Re: I need help in factorising power of quad and 3 unknown

Quote:
Originally Posted by rnck
Quote:
 Originally Posted by rnck 2) Factorize . abc - a^2b + ab^2 - a + b - c
...
Here's the answer for the quote above (ab-1) (a-b-c)

What missing is working step which i failed to even form one.....any formula / steps recommendation?
Are you sure you typed the question (or answer) correctly?
When you expand the answer, it would be $\;-\,abc\,+\,a^2b\,-\,ab^2\,-\,a\,+\,b\,+c$

April 8th, 2010, 05:56 AM   #6
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Re: I need help in factorising power of quad and 3 unknown

Quote:
 Originally Posted by tomorrow Are you sure you typed the question (or answer) correctly? When you expand the answer, it would be $\;-\,abc\,+\,a^2b\,-\,ab^2\,-\,a\,+\,b\,+c$
!
oh yea , thanks for pointing it out , i mistyped the question.
but still it is...
$\,abc\,+\,a^2b\,-\,ab^2\,-\,a\,+\,b\,-c$ (to be honest , the main reason i submit this question is because i can't get +abc after expanding it , weird)

maybe he gave wrong answer or wrong question to me.
assume if it is his mistake is there anyhow to de-expand it? (based on your equation after expanding the answer?)

 April 8th, 2010, 06:33 AM #7 Member   Joined: Feb 2010 Posts: 51 Thanks: 0 Re: I need help in factorising power of quad and 3 unknown When the question is like this, $\;-\,abc\,+\,a^2b\,-\,ab^2\,-\,a\,+\,b\,+c$ Take ab out for the first three terms and -1 for the rest, $\;ab\,(\,a\,-\,b\,-c\,)\,-\,(\,a\,-\,b\,-\,c\,)\,$ Then, you can get $(\;ab\,-1\,)\,(\,a\,-\,b\,-c\,)$ Hope that I got it correct... But if your question is this one $\,abc\,+\,a^2b\,-\,ab^2\,-\,a\,+\,b\,-c$ It would be $\,ab\,(\,a\,-\,b\,+\,c\,)\,-\,(\,a\,-b\,+c\,)$ And then, it becomes $\,(\,ab\,-\,1\,)\,(\,a\,-\,b\,+\,c\,)\,$
 April 8th, 2010, 06:48 AM #8 Senior Member   Joined: Apr 2010 Posts: 128 Thanks: 0 Re: I need help in factorising power of quad and 3 unknown I see , so the main point is to factor the multiplied terms into single terms equivalent to non-multiplied term and solve... ok , thanks. (Hopefully these two question will guide me through my maths exam)
April 8th, 2010, 06:53 AM   #9
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Re: I need help in factorising power of quad and 3 unknown

Quote:
 Originally Posted by rnck I see , so the main point is to factor the multiplied terms into single terms equivalent to non-multiplied term and solve... ok , thanks. (Hopefully these two question will guide me through my maths exam)
Not for all the time. When you practise more, you'll know how to choose the terms..

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# how to factorize two unknown with power

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