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# 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

**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) 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} + x^{2} 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}).

Hence, by observing all possibilities we got the option (c) 9x^{4} – x^{3} – 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) 9x^{4} - x^{3} - x/5 is a polynomial with a degree of 4.

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