Higher-Order Polynomial Functions

Question

Given the polynomial 1x7+6x4−6−1x61x7+6x4-6-1x6:

a) Find the degree of the term 1x71x7: 

b) Find the degree of the term 6x46x4: 

c) Find the degree of the term −6-6: 

d) Find the degree of the polynomial 1x7+6x4−6−1x61x7+6x4-6-1x6

Find the degree, leading coefficients, and the maximum number of real zeros of the polynomial.

f(x)=4x2+5−x5+3x4f(x)=4x2+5-x5+3x4

a) Degree:   

b) Leading Coefficient:   

c) Maximum number of real zeros: 

Find the degree, leading coefficients, and the maximum number of real zeros of the polynomial.

f(x)=6x6+1+4x4+2x7f(x)=6x6+1+4x4+2x7

a) Degree:   

b) Leading Coefficient:   

c) Maximum number of real zeros:

Answer 1

f(x)=4x2+5−x5+3x4f(x)=4x2+5-x5+3x4

in this polynomial equation x^5 is the largest exponent so that variable has degree 5 and leading coefficient is 1

maximum number of zero is always equal to greatest degree of the polynomial function

so x^5 maximum zero of real zero is 5