Question

A polynomial of degree 5 has the following characteristics:

• a leading coefficient 1
• a zero of multiplicity 1 at x = -3
• a zero of multiplicity 3 at x = -7
• a zero of multiplicity 1 at x = -9
Determine a possible polynomial of degree 5 that satisfies the above condition
P(x)
=

Answer 1

A polynomial of degree 5 can be written as P(x) = a(x - r1)(x - r2)...(x - rn), and a possible polynomial that satisfies the given conditions is P(x) = 1(x + 3)(x + 7)^(3)(x + 9).

Step-by-step explanation:

A polynomial of degree 5 can be written in the form:

P(x) = a(x - r1)(x - r2)...(x - rn)

Where a is the leading coefficient and r1, r2, ..., rn are the zeros of the polynomial.

From the given characteristics, we have:

P(x) = 1(x + 3)(x + 7)3(x + 9)

Expanding this polynomial would give a possible polynomial of degree 5 that satisfies the given conditions.

Learn more about Polynomial of degree 5