To determine the factors of the polynomial x² + 20, we will look for expressions that can multiply to give us this polynomial.
Firstly, we notice that x² + 20 does not factor easily into linear factors with real coefficients because it doesn’t equal zero for any real values of x. However, it can be expressed in terms of complex numbers.
One way to represent it is to recognize that the polynomial x² + 20 can be rewritten using the difference of squares:
x² + 20 = x² – (-20) = x² – (√20i)².
From this representation, we can factor it as:
(x – √20i)(x + √20i)
Thus, the factors of the polynomial x² + 20 are (x – √20i) and (x + √20i), which represent complex factors due to the presence of the imaginary unit i.
In conclusion, while x² + 20 has no real factors, it can be factored in the realm of complex numbers. This shows the beauty of polynomials as we explore different number systems!