Question

p of X is equals to x cube minus 3 X square + 5 x minus 3.of g of x equal to x square minus 2 .find q of X and r of X by division algorithm​

Answer 1

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Answer 2

$We \: have \: p(x) = x^{3}-3x^{2}+5x-3 \\and \: g(x) = x^{2} - 2$

Long division method :

x²-2)x³-3x²+5x-3(x-3

***** x³ + 0 -2x

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********* -3x²+7x-3

********* -3x²+ 0 +6

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Remainder ( 7x-9)

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Dividend p(x) = x³-3x²+5x-3,

Divisor g(x)= x²-2 ,

Quotient q(x)= x - 3 ,

Remainder r(x) = 7x - 9

$\underline { \blue { Division \: Algorithm }}$

$\boxed {\pink { Dividend = divisor \times quotient + Remainder }}$

$g(x) \times q(x) + r(x)$

$= (x^{2}-2)(x-3)+(7x-9)$

$= x^{2}(x-3)-2(x-3)+7x-9 \\= x^{3}-3x^{2}-2x+6+7x-9 \\= x^{3}-3x^{2}+5x-3\\= Dividened$

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