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Q.

Find the polynomial with degree $6$ .

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a

6 x^{4} + 7 x^{2}

b

8 x^{4} y^{2} + 7 x^{5} y^{3} - \frac{3}{5}

c

8 x^{2} y^{2} z^{2} + 7 x^{2} y^{2} z + 3 x^{4}

d

8 x^{6} y^{6} + y^{2} + 7 x^{3}

answer is C.

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Detailed Solution

It is given that the degree is 6.
We have to find the polynomial with degree 6.
In the case of a polynomial in one variable, the highest power of the variable is called the degree of the polynomial.
In the case of polynomials in more than one variable, the sum of the powers of the variables in each term is taken up and the highest sum obtained is called the degree of the polynomial.
In option (1),

6 x^{4} + 7 x^{2} :

The highest power of this expression is 4.
Then the degree is 4.
In option (2),

8 x^{4} y^{2} + 7 x^{5} y^{3} - \frac{3}{5} :

The highest power of this expression is 5+3=8.
Then the degree is 8.
In option (3),

8 x^{2} y^{2} z^{2} + 7 x^{2} y^{2} z + 3 x^{4}

.
The highest power of this expression is 2+2+2=6.
Then the degree is 6.
In option (4),

8 x^{6} y^{6} + y^{2} + 7 x^{3}

The highest power of this expression is 6+6=12.
Then the degree is 12.
Hence, the required answer is

8 x^{2} y^{2} z^{2} + 7 x^{2} y^{2} z + 3 x^{4}

Therefore, option (3) is correct.

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