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Question Number 84430 by M±th+et£s last updated on 12/Mar/20

Commented by mr W last updated on 12/Mar/20

$f (2) = 2^{2} = 4$
Commented by M±th+et£s last updated on 12/Mar/20

$t h a n k y o u s i r b u t c a n y o u t e l l m e h o w$ $d i d y o u g e t t h i s a n s w e r$
Commented by mr W last updated on 13/Mar/20

$w h a t i s a p o l y n o m i a l ?$ $a p o l y n o m i a l i s a e x p r e s s i o n c o n s i s t i n g$ $o f v a r i a b l e s a n d c o e f f i c i e n t s, t h a t$ $i n v o l v e s o n l y t h e o p e r a t i o n s o f$ $a d d i t i o n, s u b t r a c t i o n, m u l t i p l i c a t i o n,$ $a n d n o n - n e g a t i v e i n t e g e r e x p o n e n t s$ $o f v a r i a b l e s .$ $f (x) = \frac{a + 3}{x^{4}} + (b - 2) x^{- 3} + x^{n - a + b}$ $s u c h t h a t f (x) i s a p o l y n o m i a l, t h e$ $t e r m s w i t h \frac{1}{x^{4}} a n d x^{- 3} m u s t v a n i s h,$ $i . e . a = - 3 a n d b = 2 .$ $\Rightarrow f (x) = x^{n - a + b}$ $s i n c e i t i s a q u a d r a t i c p o l y n o m i a l, t h e$ $h i g h e s t e x p o n e n t o f v a r i a b l e s i s 2,$ $b u t i t h a s o n l y o n e t e r m, t h e r e f o r e$ $t h i s t e r m m u s t b e x^{2}, i . e . n - a + b = 2,$ $o r n = - 3 .$ $\Rightarrow f (x) = x^{2}$
Commented by M±th+et£s last updated on 13/Mar/20

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