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Question
Divide first polynomial by second polynomial and write the answer in the form ‘Dividend = Divisor × Quotient + Remainder’.
`5x^5 + 4x^4 - 3x^3 + 2x^2 +2;x^2-x`
Solution
5x3 + 9x2 + 6x + 8
`x^2 - x)overline(5x^5 + 4x^4 - 3x^3 + 2x^2 + 2)`
5x5 - 5x4
- +
9x4 - 3x3 + 2x2 + 2
9x4 - 9x3
- +
6x3 + 2x2 + 2
6x3 - 6x2
- +
8x2 + 2
8x2 - 8x
- +
8x + 2
Dividend = Divisor × Quotient + Remainder
`5x^5 + 4x^4 - 3x^3 + 2x^2 +2 = (x^2 - x) xx (5x^3 + 9x^2 + 6x + 8) + (8x + 2)`
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