How do you factor a problem with X^4 in it?

Question

X^4 -3X^3 + X -3

and

X^3 -1

are the problems

Answer 1

X^4 -3X^3 + X -3

factor by groupign first and last 2 terms together

= x^3(x-3) +1(x-3)

= (x-3)(x^3+1)

now factorign that last bracket as it sis a sum of 2 cubes

=(x-3)(x+1)(x^2-x+1)

X^3 -1 differnce of 2 cubes

= (x-1)(x^2 +1x +1)

Answer 2

OK.. Take a look at this.. X^4 can be split into X^2 and X^2

3 Is a Prime number, so is only divisible by itself and 1

so one half of the factored equation will be (X^2-3)

Take this out of the equation and you are left with (X^2+X)

(X^2-3)(X^2+X) = X^4 -3X^3 + X-3

X^3-1 can't be broken down, the only factor you can get out of it is 1

Answer 3

i think you have to combine like terms.  

Answer 4

I'm not so sure what you're talking about but let me give you an example

(x)^2+b+x^2+y

first multiply x times x

the problem is now x^2+b+x^2+y

                                                                

                                      

Notice how there are two x squareds?

Combine like terms

2x^2+b+y

The question is now factored

I hope this helps :)

Answer 5

(x^4) - (3*x^3) + x - 3

divide this into 2 parts

(x^4) - (3*x^3)      and        + x - 3

now, greatest common factor

x^3 (x -3)   and +1 (x-3)

and now you have common factor (x-3)

so, factors are:

(x^3 +1) and (x-3)

x^3 -1

(x-1) ( x^2 +1x +1)

the first part (x-1) you get by taking 3rd root of each value separately (x^3 --> x, and 1--> 1).

the second part: the first value (x^2) is the value of the first value (x) in the first factor (x-1) squared. the second value (+1x) is the negated product of -1 and x (from x-1). the last is the square of the second value, -1. so -1*-1=1.

now help me?

my question: how to solve 2^x + 2^-x = 5. find x.  

Answer 6

X^4 -3X^3 + X -3

take x^3 common from first two term

= x^3(x-3) +(x-3)

= (x-3)(x^3+1)

2) x^3-1

can be written as

= x^3-1^3

expand using the formula

(a^3-b^3) = (a-b)(a^2+ab+b^2)

= (x-1)(x^2+x+1)

Answer 7

it will be useless but like this

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

but this one will be useful:

x^3(x-3) +(x-3)

(x-3)(x^3+1)