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fx=4 x3+5 x2+...

Question

$f (x) = 4 x^{3} + 5 x^{2} + 9$ and $g (x, y) = 4 x^{3} y + 5 y x^{2} + 15$ . Let the degree of $f (x) and g (x, y)$ be $α$ and $β$ . Then the value of $α + β$ is

A

3

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B

4

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C

6

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D

7

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Solution

The correct option is D $7$
Degree of a polynomial = Highest power of variable.
$∴$ Degree of $f (x) = 4 x^{3} + 5 x^{2} + 9$ will be the highest power of x.
$\Rightarrow α = 3.$
Simillarly,
Degree of $g (x, y) = 4 x^{3} y + 5 y x^{2} + 15$ will be the highest power of $x$ and $y$
$∴ β = 4$
$\Rightarrow α + β = 7.$

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