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  4. These are numeric entry type questions. If the degrees of two polynomials f(x) and [f(x) ⋅ g(x)] are 6 and 18 , respectively, then the degree of g(x) is

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Q. These are numeric entry type questions.
If the degrees of two polynomials $f(x)$ and $[f(x) \cdot g(x)]$ are 6 and 18 , respectively, then the degree of $g(x)$ is______

Polynomials and Square Roots of Algebraic Expressions

Solution:

Degree of $f(x) \cdot g(x)=$ Degree of $f(x)+$ Degree of $g(x)$
$\Rightarrow 6+$ Degree $g(x)=18$
$\Rightarrow$ Degree of $g(x)=18-6=12$