Question

f(z)=Z⁵-6Z⁴+z f(z)=6z²+10z-7. Subtract the second polynomial from the first polynomial and find the degree of the resultant polynomial.

Answer 1

first polynomial , f(z) = z^5 - 6z^4 + z
2nd polynomial , f(z) = 6z^2 + 10z - 7

subtract 2nd polynomial from the 1sy polynomial,
e.g., z^5 - 6z^4 + z - (6z^2 + 10z - 7)

= z^5 - 6z^4 + z - 6z^2 - 10z + 7

= z^5 - 6z^4 - 6z^2 - 9z + 7

degree of any polynomial is the highest power of variable term.
for example , if $P(x)=a_nx^n+a_{n-1}x^{n-1}+a_{(n-2}x^{n-2}+......a_0$ is the polynomial of nth degree because highest power of x is n.

similarly , degree of resultant polynomial is 5.
because we are seeing that highest power of x is 5.

hence, degree of polynomial is 5.

Answer 2

Hi ,

Given two polynomials are

F(z) = z^5 - 6z⁴ + z ,

f(z) = 6z² + 10z - 7

Let the resultant polynomial p(z)

p(z) = F(z) - f(z)

= z^5 - 6z⁴ + z - ( 6z² + 10z - 7 )

= z^5 - 6z⁴ + z - 6z² - 10z + 7

= z^5 - 6z⁴ - 6z² - 9z + 7

Therefore ,

Resultant polynomial = p(z)

= z^5 - 6z⁴ - 6z² - 9z + 7

Degree of p(z) = Heighest power

of z in p( z )

= 5

I hope this helps you.

: )