Verify the division algorithm i.e., Dividend = Divisor × Quotient… - Vidyadip

Question

Verify the division algorithm i.e., Dividend = Divisor × Quotient + Remainder, in the following. Also write the quotient and remainder.
Dividend: $34 x-22 x^3-12 x^4-10 x^2-75$
Divisor: $3 x+7$

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Answer

Quotient $= -4 x^3+2 x^2-8 x+30$
Remainder $= -285$
Divisor $= 3x + 7$
Divisor × Quotient + Remainder $=(3 x+7)\left(-4 x^3+2 x^2-8 x+30\right)-285$
$=-12 x^4+6 x^3-24 x^2+90 x-28 x^3+14 x^2-56 x+210-285$
$=-12 x^4-22 x^3-10 x^2+34 x-75$
= Dividend
Divisor × Quotient + Remainder = Dividend
Hence verified.

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