Find all the zeros of the function and write the polynomial as a product of linear factors. f(x) = x² + 25.

Solution:

A polynomial is a type of expression. Before we discuss polynomials, we should know about expressions.

An expression is a mathematical statement without an equal-to sign (=).

 "A polynomial is a type of expression in which the exponents of all variables should be a whole number."

The zeroes of the function x² + 25 can be obtained by equating it to zero.

f(x) = x² + 25 = 0

x² = -25

x = ± 5i

We can write the polynomial in factors form as follows:

f(x) = (x + 5i)(x - 5i)

Find all the zeros of the function and write the polynomial as a product of linear factors. f(x) = x² + 25.

Summary:

The zeroes of the function are f(x) = ± 5i and the function can be expressed as a product of linear factors as f(x) = (x + 5i)(x - 5i). The number of zeros of the function depends on finding the number of linear factors.