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amcavoy
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How can I factor the following polynomial?
[tex]x^5+x+1[/tex]
Thanks for your help.
[tex]x^5+x+1[/tex]
Thanks for your help.
eNathan said:like dextercioby said, concerning (x^5 + x + 1) it cannot be factored. Some things are already in their simplest form. X^2 is one monomial, x is one monomial, and 1 is one monomial. There are no like terms, thus they cannot be factored.
huan.conchito said:[tex](x^3-x^2+1)(x^2+x+1)=(x^5+x+1)[/tex]
like dextercioby said, concerning (x^5 + x + 1) it cannot be factored. Some things are already in their simplest form. X^2 is one monomial, x is one monomial, and 1 is one monomial. There are no like terms, thus they cannot be factored.
huan.conchito said:took me a while to get it right
[tex](x^3-x^2+1)(x^2+x+1)[/tex]=[tex](x^5+x+1)[/tex]=[tex]x(x^4+1)+1[/tex]
The first step in factoring x^5+x+1 is to check if there are any common factors among the terms. In this case, there are no common factors. Next, we can try to factor by grouping. However, since there are only three terms, this method is not applicable. The final step is to use the quadratic formula to find the roots of the polynomial. Unfortunately, in this case, the polynomial does not have any real roots. Therefore, x^5+x+1 is not factorable.
No, the difference of squares method can only be used when there are two terms in the polynomial. In this case, there are three terms, so this method is not applicable.
No, synthetic division can only be used to divide a polynomial by a linear factor. In this case, the polynomial x^5+x+1 does not have any linear factors, so synthetic division cannot be used to factor it.
A polynomial is considered prime if it cannot be factored into two polynomials with integer coefficients. In other words, if the polynomial does not have any factors other than 1 and itself, it is considered prime. In the case of x^5+x+1, since it cannot be factored, it is considered a prime polynomial.
No, there is no general formula for factoring polynomials. However, there are various methods and techniques that can be used depending on the type of polynomial. It is important to first check for any common factors and then try different methods, such as grouping, difference of squares, or using the quadratic formula to find the roots, to factor the polynomial.