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

# (a) 5x^{4}+ square root of 4x

# (b) x^{5} – 6x^{4} + 14x^{3} + x^{2}

# (c) 9x^{4} – x^{3} – x/5

# (d) 2x^{4} – 6x^{4} + 14/x

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

## Answer: Option (c) 9x^{4} – x^{3} – x/5, is the correct answer, and 9x^{4} – x^{3} – x/5 is a polynomial with a degree of 4.

Let us proceed step by step.

**Explanation:**

Let us see all the given options in detail.

**(a)** 5x^{4}+ 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)** x^{5} – 6x^{4} + 14x^{3} + x2; cannot be the polynomial of degree 4 as maximum power is given as 5, hence the degree will be equal to 5.

**(c)** 9x^{4} – x^{3} – 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)** 2x^{4} – 6x^{4} + 14/x; cannot be the polynomial as it violates the definition of the polynomial as the variable is having a negative power ( x^{-1}).