Find the degree of this polynomial Let fx 2x2x 1x 23x2 1

Find the degree of this polynomial

Let f(x) = 2x^2(x - 1)(x + 2)^3(x^2 + 1)^2 Find the degree of this polynomial What is the leading coefficient of this polynomial function? What is the leading term of this polynomial function? List the zeros of f and indicate their multiplicity.

Solution

f(x) = 2x^2 ( x - 1) ( x+2)^3 ( x^2 + 1)^3

a) degree of polynomial is the highest exponent of the polynomial

hence highest exponent of the polynomial is 12

b) leading coefficient of the polynomial is 2

c) leading term of the polynomial is the first term

leading term is 2x^12

d) to find zeros of the function set function to 0

2x^2 ( x - 1) ( x+2)^3 ( x^2 + 1)^3 = 0

zeros are :

x= 0 ( multiplicity 2 )

x = 1 ( multiplicity 1 )

x = -2 ( multiplicity 3 )

x = + - i ( complex zero )

x =