If x -1- then find the quotient of x 5 - x 4 - x 3 - x 2 x 3 - x 2 -x-1

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Standard XII

Mathematics

How to Find the Inverse of a Function

If x -1, th...

Question

If $x \neq - 1$ , then find the quotient of $\frac{x^{5} + x^{4} + x^{3} + x^{2}}{x^{3} + x^{2} + x + 1}$

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Solution

Just take $x^{2}$ as commun factor from $(x^{5} + x^{4} + x^{3} + x^{2})$ = $x^{2} (x^{3} + x^{2} + x + 1)$

Simply commun factors are cancelled and we get

$\frac{x^{2} (x^{3} + x^{2} + x + 1)}{(x^{3} + x^{2} + x + 1)} = x^{2}$

quotient = $x^{2}$

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Similar questions

Q. If

x \neq - 1

, then find the equation of

\frac{x^{5} + x^{4} + x^{3} + x^{2}}{x^{3} + x^{2} + x + 1} = 1

Q. If

x

is a rational number satisfying

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

= \frac{31}{32} .

Then

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

\int (x + x^{2} + x^{3} + x^{4})

dx is equal to

$x^{5} + x^{4} + x^{3} + x^{2} + x + 1$ by $x^{3} + 1$

If $(1 - x) (1 + x + x^{2} + x^{3} + x^{4})$ is $\frac{31}{32}$ and $x$ is a rational number. Find the value of $1 + x + x^{2} + x^{3} + x^{4} + x^{5}$ .

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If x≠−1, then find the quotient of x5+x4+x3+x2x3+x2+x+1

Just take x2 as commun factor from (x5+x4+x3+x2)=x2(x3+x2+x+1)Simply commun factors are cancelled and we get x2(x3+x2+x+1)(x3+x2+x+1)=x2quotient = x2

If $x \neq - 1$ , then find the quotient of $\frac{x^{5} + x^{4} + x^{3} + x^{2}}{x^{3} + x^{2} + x + 1}$

Just take $x^{2}$ as commun factor from $(x^{5} + x^{4} + x^{3} + x^{2})$ = $x^{2} (x^{3} + x^{2} + x + 1)$

Simply commun factors are cancelled and we get

$\frac{x^{2} (x^{3} + x^{2} + x + 1)}{(x^{3} + x^{2} + x + 1)} = x^{2}$

quotient = $x^{2}$