Simplify the polynomial and write it in standard form:
${(x}^{3} + 1) (- 2 x + 2) + 2 x^{2} (4 x^{2} + 1)$

5 x^{4} + 3 x^{3} + 2 x^{2} - 2 x + 3

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6 x^{4} + 2 x^{3} + 2 x^{2} - 2 x + 2

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x^{4} + 2 x^{3} + 6 x^{2} - 2 x + 3

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6 x^{4} + 3 x^{3} + 2 x^{2} + 4

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Solution

The correct option is A $6 x^{4} + 2 x^{3} + 2 x^{2} - 2 x + 2$
We have, $(x^{3} + 1) (- 2 x + 2) + 2 x^{2} (4 x^{2} + 1)$

$= x^{3} (- 2 x + 2) + 1 (- 2 x + 2) + 8 x^{4} + 2 x^{2}$

$= - 2 x^{4} + 2 x^{3} - 2 x + 2 + 8 x^{4} + 2 x^{2}$

$= 6 x^{4} + 2 x^{3} + 2 x^{2} - 2 x + 2$

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Similar questions

f (x) = \sqrt{\frac{x^{4} - 2 x^{3} + 3 x^{2} - 2 x + 2}{2 x^{2} - 2 x + 1}}

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

(iv) $x^{1000} - 1$

(v) $\frac{1}{\sqrt{2}} x^{2} - \sqrt{2} x + 2$

(vi) $x^{- 2} + 2 x^{- 1} + 3$

(vii) $1$

(viii) $\frac{- 3}{5}$

(ix) $\frac{x^{2}}{2} - \frac{2}{x^{2}}$

(x) $\sqrt[2]{2} x^{2} - 8$

(xi) $\frac{1}{2 x^{2}}$

(xii) $\frac{1}{\sqrt{5}} x^{\frac{1}{2}} + 1$

(xiii) $\frac{3}{5} x^{2} - \frac{7}{3} x + 9$

(xiv) $x^{4} - x^{\frac{3}{2}} + x - 3$

(xv) $2 x^{3} + 3 x^{2} + \sqrt{x} - 1$

q (x)

(x^{4} + x^{3} - 2 x^{2} + x - 1)

(x - 1)

- 3 (x^{3} - x^{2} - 2 x - 5) - (4 x^{3} - 7 x - 1)

2 x^{7} - 128 x

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