What is the degree of polynomial $P$ defined by :
$P (x) = - 5 (x - 2) (x^{3} + 5) + x^{5}$ ?

2

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3

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4

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5

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Solution

The correct option is D $5$
Solve the polynomial as follows:
$- 5 (x - 2) (x^{3} + 5) + x^{5}$
$= (- 5 x + 10) (x^{3} + 5) + x^{5}$
$= - 5 x^{4} - 25 x + 10 x^{3} + 50 + x^{5}$ or
$= x^{5} - 5 x^{4} + 10 x^{3} - 25 x + 50$
Since the highest degree of its term is the degree of a polynomial and here the highest degree is $5$ .
Hence, the degree of the given polynomial is $5$ .

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Similar questions

Degree of the polynomial p(x) = 4x⁴ + 2x³ + x⁵ + 2x + 7 is:

p (x) = 2 x + \frac{3}{2} x^{3} - 7

Which of the following expressions are polynomials? In case of a polynomial, write its degree.

(i) $x^{5} - 2 x^{3} + x + \sqrt{3}$

(ii) $y^{3} + \sqrt{3} y$

(iii) $t^{2} - \frac{2}{5} t + \sqrt{5}$

Find the polynomial from the given information.

Quotient = x^{3} + 2 x

Divisor = x^{2} + \frac{1}{2} x

Remainder = 5

P (x) = {(\sqrt{x^{5} - 1} + x)}^{7} - {(\sqrt{x^{5} - 1} - x)}^{7}

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