Find the H-C-F- of x 2- x -1 and x 4- x 2-1 by using the division method- A- x2-x-1B- x2-x-1C- x2-x-1D- x2-2 x-1

The correct option is A x^2+x+1x^2+x+1 nbsp;) x^4+0x^3+x^2+1(x^2 x+1 x^4+x^3+x^2 x ...

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Byju's Answer

Standard X

Mathematics

GCD of Polynomials

Find the H.C....

Question

Find the H.C.F. of $(x^{2} + x + 1)$ and $(x^{4} + x^{2} + 1)$ by using the division method.

x^{2} + x + 1

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x^{2} + x - 1

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x^{2} - x + 1

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x^{2} + 2 x + 1

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Solution

The correct option is A $x^{2} + x + 1$
$x^{2} + x + 1) x^{4} + 0 x^{3} + x^{2} + 1 (x^{2} - x + 1 x^{4} + x^{3} + x^{2} - - - - -------------- - - x^{3} + 0 x^{2} + 0 x + 1 - x^{3} - x^{2} - x + + + - -------------- - x^{2} + x + 1 x^{2} + x + 1 - - - - ------------ - 0$

Therefore, H.C.F $= x^{2} + x + 1$

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Similar questions

The simplest form of $\frac{(x^{3} - 1)}{(x^{2} - 1)}$ is

Q. x + 1 is a factor of the polynomial
(a) x³ + x²– x + 1
(b) x³ + x² + x + 1
(c) x⁴ + x³ + x² + 1
(d) x⁴ + 3x³ + 3x² + x + 1

$x + 1$ is a factor of the polynomial
$A .$ $x^{3} + x^{2} - x + 1$
$B .$ $x^{3} + x^{2} + x + 1$
$C .$ $x^{4} + x^{3} + x^{2} + 1$
$D .$ $x^{4} + 3 x^{3} + 3 x^{2} + x + 1$

\int \frac{d x}{(x + 1) \sqrt{x^{2} - 1}} =

Q. What is the quotient obtained when

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

is divided by

x^{2} + 2 x - 3

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Find the H.C.F. of (x2+x+1) and (x4+x2+1) by using the division method.

Find the H.C.F. of $(x^{2} + x + 1)$ and $(x^{4} + x^{2} + 1)$ by using the division method.