Using synthetic division- solve x4 - 2x3 - 3x2 - 4x - 5 - x - 2-Write the quotient and the remainder-

Synthetic division: (x^4 + 2x^3 + 3x^2 + 4x + 5) ÷ (x + 2) nbsp;Dividend = x^4 + 2x^3 + 3x^2 + 4x + 5 ∴ nbsp;Coefficient form of dividend = (1, 2, 3, 4, 5) n ...

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Standard IX

Mathematics

Long Division of Polynomials

Using synthet...

Question

Using synthetic division, solve $(x^{4} + 2 x^{3} + 3 x^{2} + 4 x + 5) \div (x + 2)$ .
Write the quotient and the remainder.

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Solution

Synthetic division:
$(x^{4} + 2 x^{3} + 3 x^{2} + 4 x + 5) \div (x + 2)$
$Dividend = x^{4} + 2 x^{3} + 3 x^{2} + 4 x + 5$
$∴ Coefficient form of dividend = (1, 2, 3, 4, 5)$
$Divisor = x + 2$
$∴ Opposite of + 2 is -2$

$Coefficient form of quotient = (1, 0, 3, - 2)$
$∴ Quotient = x^{3} + 3 x - 2,$
$Remainder = 9$

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Using synthetic division, solve (x4+2x3+3x2+4x+5)÷(x+2). Write the quotient and the remainder.

Synthetic division: (x4+2x3+3x2+4x+5)÷(x+2) Dividend=x4+2x3+3x2+4x+5 ∴Coefficient form of dividend =(1,2,3,4,5) Divisor=x+2 ∴Opposite of + 2 is -2 Coefficient form of quotient=(1,0,3,−2) ∴ Quotient=x3+3x–2, Remainder = 9

Using synthetic division, solve $(x^{4} + 2 x^{3} + 3 x^{2} + 4 x + 5) \div (x + 2)$ .
Write the quotient and the remainder.