Factoring Quadratic Equations

**Nismo** · November 14th 2009, 11:20 PM

Can i get some help these are the last 5 problems that im stuck with. -_-

(COMPLETED)1) (X-Y)^3 +27

(COMPLETED)2) X^2-A^2+X-A

(COMPLETED)3) 3x^(-3/2) - 12x^(1/2)

4) x^(1/2) (x-4)^(-1/2) +3x^(-1/2) (x-4)^(-3/2)

(COMPLETED)5) x^(2n+2) +x^(n+2)-56x^2

for 3 im think its (3x^-3/2)(1-4x^2) but yeah im not sure. but everything else im clueless at right now. thxs for hte help!

**Bacterius** · November 14th 2009, 11:25 PM

1) $27 = 3^3$ , difference of two cubes.

2) If you factorize (difference of two squares) the two first terms, you get $(x - a)(x + a) + (x - a)$ . Can you see the common factor ?

Now I have no time for the other ones, sorry. I did 40% of the job though !

**earboth** · November 14th 2009, 11:43 PM

Originally Posted by Nismo

...

3) 3x^(-3/2) - 12x^(1/2)

...

for 3 im think its (3x^-3/2)(1-4x^2) but yeah im not sure. but everything else im clueless at right now. thxs for hte help!

1. Your result is OK but unfinished:

2. When factoring out a term from a sum you have to divide each summand by the factor. In your case:

$3x^{-\frac32} - 12x^{\frac12} = 3x^{-\frac32} \left(\dfrac{3x^{-\frac32}}{3x^{-\frac32}} - \dfrac{12x^{\frac12}}{3x^{-\frac32}} \right) = 3x^{-\frac32}\left(1-4x^2\right)$

3. The sum in the bracket is a difference of squares which can be factorized immediately. Therefore the result is:

$3x^{-\frac32} - 12x^{\frac12} = 3x^{-\frac32}(1-2x)(1+2x)$

**Nismo** · November 15th 2009, 05:05 PM

thxs earboth i just noticed that i didnt factor it all the way out -_- it was like 12ish i think when i was doing this.. -_-

also for that 1st problem i was getting

((x-y)-3)(x^2-2xy+y^2+3x-3y+9) but it looks wrong. is it?

and for 2 i actually did factor out to that

but didnt know where to go from thier. i thought it would be somthing like

(x-a)((1+1)(1-1))-1 but i dont think its that.

**Krahl** · November 15th 2009, 05:28 PM

1. $a^3+b^3= (a+b)(a^2-ab+b^2)$
you need to leave (x-y) intact and not multiply it out.

5. Take out a factor of x^2 and then it may look familiar.

Originally Posted by Nismo

and for 2 i actually did factor out to that

but didnt know where to go from thier. i thought it would be somthing like

(x-a)((1+1)(1-1))-1 but i dont think its that.

take out (x-a)

(x-a)(x+a)+(x-a)=(x-a)((x+a)+1)

**Nismo** · November 15th 2009, 07:10 PM

Originally Posted by Krahl

1. $a^3+b^3= (a+b)(a^2-ab+b^2)$
you need to leave (x-y) intact and not multiply it out.

5. Take out a factor of x^2 and then it may look familiar.

take out (x-a)

(x-a)(x+a)+(x-a)=(x-a)((x+a)+1)

i see how you did it, and that it does distribute out to the x^2-y^2+x-a but im still getting marked wrong on it o_0

wouldnt it just be (x-a)(x+a+1) without the prenthesis in side?

**ukorov** · November 15th 2009, 07:55 PM

not sure about #4. this is what i am up to

$\frac{(x - 3)(x - 1)}{\sqrt{x^2 - 4x}(x - 4)}$

**Krahl** · November 16th 2009, 02:15 PM

Originally Posted by Nismo

i see how you did it, and that it does distribute out to the x^2-y^2+x-a but im still getting marked wrong on it o_0

wouldnt it just be (x-a)(x+a+1) without the prenthesis in side?

If your doing one of them online things then sometimes extra brackets do effect answers. try it without the brackets see what it says

**Nismo** · November 16th 2009, 05:01 PM

naw found out my teacher did his coding wrong. and he said it was right! thxs for the help! although i still gotta finish the rest of the problems!! ha.

**Krahl** · November 17th 2009, 04:01 PM

5. Take out a factor of x^2 and then it may look familiar.

x^(2n+2) +x^(n+2)-56x^2= $x^2x^{2n}+x^2x^n-56x^2$
$=x^2(x^{2n}+x^n-56)=x^2((x^n)^2+x^n-56)$

can you factorise the stuff in the brackets?
hint y^2+y-56=(y+8)(y-7)

**Nismo** · November 17th 2009, 09:09 PM

Originally Posted by Krahl

5. Take out a factor of x^2 and then it may look familiar.

x^(2n+2) +x^(n+2)-56x^2= $x^2x^{2n}+x^2x^n-56x^2$
$=x^2(x^{2n}+x^n-56)=x^2((x^n)^2+x^n-56)$

can you factorise the stuff in the brackets?
hint y^2+y-56=(y+8)(y-7)

haha i actually got that far last night with the x^2((x^n)^2+x^n-56) but i didnt know how to factor it out from thier although i knew it had to deal with 7 and 8. but yeah i got it fianlly! thxs!

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