What is the factor of X power 4 +x square + 1
(x^2+1)^2 = x^4+2x^2+1
so,
x^4+x^2+1 = (x^2+1)^2 - x^2
= (x^2+1+x)(x^2+1-x)
No linear factors with rational coefficients.
To find the factor of the expression X^4 + X^2 + 1, we can use the method of factoring by grouping.
Step 1: Factor out X^2 from the expression:
X^4 + X^2 + 1 = X^2(X^2 + 1) + 1
Step 2: Notice that the expression inside the parentheses is in the form of a quadratic equation, which cannot be factored further.
Therefore, the factor of X^4 + X^2 + 1 is X^2 + 1.
To find the factors of the expression x^4 + x^2 + 1, we need to determine if it can be factored further. Unfortunately, this expression cannot be factored using real numbers. It is a prime polynomial, meaning it has no factors other than 1 and itself over the real number system.
However, it can be factored using complex numbers. By using the concept of complex roots, we can rewrite the expression as a product of two quadratic factors:
x^4 + x^2 + 1 = (x^2 + x + 1)(x^2 - x + 1)
These quadratic factors cannot be factored further over the real or complex numbers. Therefore, the factors of x^4 + x^2 + 1 are (x^2 + x + 1) and (x^2 - x + 1).