What is the degree of the polynomial $5 x^{3} - 2 x (x^{2} + 3 x) - 3 x^{3} + 6 x^{2} ?$

0

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1

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Not defined

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None of the above

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Solution

The correct option is C Not defined
$Need to Find: - --------------- -$
Degree of the polynomial $5 x^{3} - 2 x (x^{2} + 3 x) - 3 x^{3} + 6 x^{2}$

As the given polynomial is not in standard form, we'll simplify it and express it in standard form first.

$5 x^{3} - 2 x (x^{2} + 3 x) - 3 x^{3} + 6 x^{2}$
Opening the bracket

$= 5 x^{3} - 2 x \cdot x^{2} - 2 \cdot 3 \cdot x \cdot x - 3 x^{3} + 6 x^{2}$

$= 5 x^{3} - 2 x^{3} - 6 x^{2} - 3 x^{3} + 6 x^{2}$ $[∵ a^{m} \cdot a^{n} = a^{m n}]$
Now, combining the like terms

$= (5 x^{3} - 2 x^{3} - 3 x^{3}) + (- 6 x^{2} + 6 x^{2})$

$= (5 x^{3} - 5 x^{3}) + 0$ $[∵ - 2 x^{3} - 3 x^{3} = - 5 x^{3} and - 6 x^{2} + 6 x^{2} = 0]$

$= 0$

As a result, given polynomial is a $zero polynomial - ------------------ -$ and we know that degree of a $zero polynomial - ------------------ -$ is $not defined - ------------ - .$

Therefore, option (c.) is the correct choice.

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