Which algebraic expression is a polynomial with a degree of 4?
(a) 5x⁴+ square root of 4x
(b) x⁵ - 6x⁴ + 14x³ + x²
(c) 9x⁴ - x³ - x/5
(d) 2x⁴ - 6x⁴ + 14/x

Solution:

A polynomial is defined as an algebraic expression whose maximum power is a non-negative integer.

Let us see all the given options in detail.

(a) 5x⁴+ square root of 4x cannot be the polynomial as it violates the definition of the polynomial as the variable is having a fractional power (x^1/2).

(b) x⁵ - 6x⁴ + 14x³ + x² cannot be the polynomial of degree 4 as maximum power is given as 5, hence the degree will be equal to 5.

(c) 9x⁴ - x³ - x/5 is the polynomial of degree 4 as maximum power is given as 4 and it also satisfies the definition of the polynomial.

(d) 2x⁴ - 6x⁴ + 14/x cannot be the polynomial as it violates the definition of the polynomial as the variable is having a negative power ( x^-1).

Hence, by observing all possibilities we got the option (c) 9x⁴ – x³ – x/5 as the correct answer and is a polynomial with a degree of 4.

Which algebraic expression is a polynomial with a degree of 4?

Summary:

Option (c) 9x⁴ - x³ - x/5 is a polynomial with a degree of 4.