Question

which among the following is a cubic polynomial
(a) (y)⅓ + 2
(b) z³-2z²+3z-6
(c) 1/x³
(d) all of the above ​

Answer 1

$\underline { \pink { Polynomial }}$

An algebraic expression in which the variables involved have only non - negative integral powers is called polynomial.

$\underline { \pink {Degree\:of \:the \: Polynomial }}$

The degree of a polynomial is the highest degree of its variable term.

$\underline { \pink { Cubic \: polynomial:}}$

$A \: polynomial \:of \: degree \:\blue {3} \:is \\called \:\pink {Cubic \: Polynomial }.$

$(a) y^{\frac{1}{3}} + 2 \: is \: not \: a \\polynomial\\because \: the \: first \:term\\ \:y^{\frac{1}{3}} \:is \: a \: term \:with \:an \:exponent\\that \:is \: not \:a \: non - negative \: integer \\i.e., (\frac{1}{3} )$

$(b)\: \pink { z^{3} - 2z^{2} + 3z - 6 } \:is \: a \\polynomial$

$Degree \: of \: the \: polynomial \: is \: 3$

$\green { It \: is \: a \:cubic \: polynomial . }$

$(c) \frac{1}{x^{3}} \: is \: not \: a \\polynomial\\because \: x^{-3} \:\:has\\ a \:negative \: exponent \\i.e., (-3)$

$(d) \: All \: the \: above$

Therefore.,

$Option \green { ( b) } \: is \: a \: cubic \\ polynomial .$

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