Q. 1 E4.5( 2 Votes )

# Choose the correct answer for the following:

The degree of the polynomial x^{2} – 5x^{2}y^{3} + 30x^{3} y^{4} – 576xy is

A. –576

B. 4

C. 5

D. 7

Answer :

x^{2} – 5x^{2}y^{3} + 30x^{3} y^{4} – 576xy is a polynomial in variable x and y.

**Term 1:** x^{2} variable x, power of x is 2. Hence the power of the term is **2**.

**Term 2:** – 5x^{2}y^{3} the variables are x and y; the power of x is 2 and the power of y is 3.

Hence the power of the term –5x^{2}y^{3} is 2 + 3 = **5** [Sum of the exponents of variables x and y ].

**Term 3:** 30x^{3}y^{4} the variables are x and y; the power of x is 3 and the power of y is 4. Hence the power of the term 30x^{3}y^{4} is 3 + 4 = **7** [Sum of the exponents of variables x and y ].

**Term 4:** – 576xy the variables are x and y; the power of x is 1 and the power of y is 1. Hence the power of the term -576xy is 1 + 1 = **2** [Sum of the exponents of variables x and y ].

So the highest power is 7,hence the degree of the polynomial is 7.

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