Find a polynomial f(x) of degree 5 that has the following zeros.

-9, 5, -7, 4, 8

f(x)=

-9, 5, -7, 4, 8

f(x)=

1 Answers

Best Answer

Step 1

The Factor Theorem for a non-zero polynomial p states that, if c is any real number, then,

c is a zero of p iff (x-c) is a factor of p(x)

Step 2

The polynomial f of degree 5 with the given zeros can be formulated as follows. The degree of the factors must add up to 5.

f(x)=(x-(-9))(x-5)(x-(-7))(x-4)(x-8)

f(x)=(x+9)(x-5)(x+7)(x-4)(x-8)

The Factor Theorem for a non-zero polynomial p states that, if c is any real number, then,

c is a zero of p iff (x-c) is a factor of p(x)

Step 2

The polynomial f of degree 5 with the given zeros can be formulated as follows. The degree of the factors must add up to 5.

f(x)=(x-(-9))(x-5)(x-(-7))(x-4)(x-8)

f(x)=(x+9)(x-5)(x+7)(x-4)(x-8)