Dividend=x5+x3+x2 2x+4Index nbsp;form=x5+0 nbsp;x4+x3+x2 2x+4Coefficient nbsp;form=1, nbsp;0, nbsp;1, nbsp;1, nbsp; 2, nbsp;4Comparing nbsp;th ...

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Framing Algebraic Equations

x5+x3+x2-2 x+...

Question

(x⁵ + x³ + x² $-$ 2x + 4) $\div$ (x + 3)

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Solution

$Dividend = x^{5} + x^{3} + x^{2} - 2 x + 4 Index form = x^{5} + 0 x^{4} + x^{3} + x^{2} - 2 x + 4 Coefficient form = (1, 0, 1, 1, - 2, 4) Comparing the divisor x + 3 with x - a, we get a = - 3$

$Now, quotient in coefficient form = (1, - 3, 10, - 29, 85) ∴ Quotient = x^{4} - 3 x^{3} + 10 x^{2} - 29 x + 85 in the variable x Remainder = - 251 ∴ x^{5} + x^{3} + x^{2} - 2 x + 4 = (x + 3) (x^{4} - 3 x^{3} + 10 x^{2} - 29 x + 85) - 251$

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(x^{5} + x^{3} + x^{2} - 2 x + 4) \div (x + 3)

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