Dividend=x3+2x2+x+2Index nbsp;form=x3+2x2+x+2Coefficient nbsp;form=1, nbsp;2, nbsp;1, nbsp;2Comparing nbsp;the nbsp;divisor nbsp;x 1 nbsp;with ...

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Byju's Answer

Standard XII

Mathematics

Monotonicity in an Interval

x3+2 x2+x+2 ÷...

Question

(x³ + 2x² + x + 2) $\div$ (x $-$ 1)

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Solution

$Dividend = x^{3} + 2 x^{2} + x + 2 Index form = x^{3} + 2 x^{2} + x + 2 Coefficient form = (1, 2, 1, 2) Comparing the divisor x - 1 with x - a, we get a = 1$

$Now, quotient in coefficient form = (1, 3, 4) ∴ Quotient = x^{2} + 3 x + 4 in the variable x Remainder = 6 ∴ x^{3} + 2 x^{2} + x + 2 = (x - 1) (x^{2} + 3 x + 4) + 6$

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Similar questions

$(x + 1)$ is a factor of the polynomial
(a) $x^{3} - 2 x^{2} + x + 2$ (b) $x^{3} + 2 x^{2} + x - 2$
(c) $x^{3} + 2 x^{2} - x - 2$ (d) $x^{3} + 2 x^{2} - x + 2$

If dividend = $x^{4} + x^{3} - 2 x^{2} + x + 1$ , divisor = $x - 1$ and remainder = 2. Find the quotient q(x)

Q. If dividend =

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

, divisor

= x - 1

and remainder

= 2

, then the quotient will be .

$If the dividend = x^{4} + x^{3} - 2 x^{2} + x + 1, divisor = x - 1 and remainder = 2, then find the quotient q(x) .$

When $x^{4} + x^{3} - 2 x^{2} + x + 1$ is divided by x-1, the remainder is 2 and the quotient is q(x). Find q(x).

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(x3 + 2x2 + x + 2) ÷ (x - 1)

Dividend=x3+2x2+x+2Index form=x3+2x2+x+2Coefficient form=1, 2, 1, 2Comparing the divisor x-1 with x-a, we get a=1 Now, quotient in coefficient form=1, 3, 4∴Quotient = x2+3x+4 in the variable xRemainder = 6∴ x3+2x2+x+2 = x-1x2+3x+4 +6

(x³ + 2x² + x + 2) $\div$ (x $-$ 1)