is it a polynomial? x^3 −2x^2 +(√x^2 )+10


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Question Number 206037 by Davidtim last updated on 05/Apr/24

$i s i t a p o l y n o m i a l ?$ $x^{3} - 2 x^{2} + \sqrt{x^{2}} + 10$
	Answered by Frix last updated on 05/Apr/24
	$f(x)=x^3 −2x^2 +(√x^2 )+10 x∈R ⇒ (√x^2 )=∣x∣ ⇒ f(x)= { ((x^3 −2x^2 −x+10; x<0)),((x^3 −2x^2 +x+10; x≥0)) :} This is not a polynomial.$
	$f (x) = x^{3} - 2 x^{2} + \sqrt{x^{2}} + 10$ $x \in R \Rightarrow \sqrt{x^{2}} =∣ x ∣$ $\Rightarrow$ $f (x) = {\begin{cases} x^{3} - 2 x^{2} - x + 10; x < 0 \\ x^{3} - 2 x^{2} + x + 10; x ⩾ 0 \end{cases}$ $This is not a polynomial .$
	Answered by BaliramKumar last updated on 05/Apr/24

	$yes$
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