need help for math homework.

Question

Find the quotient and remainder when  is divided by .

Answer 1

I assume you know how to divide polynomials in general. The trick to dividing polynomials when a term is missing is to add in the missing term with a coefficient of zero.

e.g. t⁴ + 0t³ - t² + 3t -7 then divide in the usual manner.

The answer I got is t² + 3t remainder -21t -7

Answer 2

t^2 + 3t

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t^2 - 3t + 8 | t^4 + 0t^3 - t^2 + 3t - 7

t^4 - 3t^3 + 8t^2

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3t^3 - 9t^2 + 3t - 7

3t^3 - 9t^2 + 24t

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-21t - 7

check: (t^2 + 3t)(t^2 - 3t + 8) - 21t - 7 =

t^4 - 3t^3 + 8t^2

+ 3t^3 - 9t^2 + 24t - 21t - 7 =

t^4 - t^2 + 3t = 7 which is the same dividend...