Question

Determine the maximum number of zeros of the polynomial function:
(5x^3 + 2x^2 - 9)(x^7 + 2x + 6)

Answer 1

Maximum number? You mean of real zeroes. The total number will be equal to the highest exponent on the variable.

What happens when you multiply that x^3 with that x^7?

Answer 2

21

Answer 3

Ah, no don't multiply the exponents.

If you multiply a power with a power (of the same base), you add the exponents.

Answer 4

\(\large x^a \cdot x^b = x^{a+b}\)

Answer 5

So it will be 10

Answer 6

Right.

Do some research on "Fundamental Theorem of Algebra" to learn more.