Question

Find the difference of f(x) and g(x) if f(x) = 5x^4 + 2x^3 + 3x^2 + 1 and

g(x) = 7x^3+ 4x^2+ 3
a. Is f(x) a polynomial? If not, give an explanation.
b. Is g(x) a polynomial? If not, give an explanation.
c. Is the difference a polynomial? If not, give an explanation.
d. If the difference is a polynomial, identify the coefficient of the x2 term.

Pls help with this please !!

Answer 1

Explanation:

Polynomial is sum of powers in one or more variables multiplied by coefficient.

a) f(x) is a polynomial of degree 4

b) g(x) is a polynomial of degree 3

c) difference = 5x⁴ +2x³ +3x² + 1 - [7x³ + 4x² + 3]

= 5x⁴ + 2x³ + 3x² + 1 - 7x³ - 4x² - 3

= 5x⁴ + 2x³ - 7x³ + 3x² - 4x² +1 - 3

= 5x⁴ - 5x³ - x² - 2