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Question
Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm g(x) = 2x2 − x + 3, f(x) = 6x5 − x4 + 4x3 − 5x2 − x − 15
Solution
3x2 + x2 − 2x − 5
`2x^2 - x + 3)overline(6x^5 - x^4 + 4x^3 - 5x^2 - x - 15)`
6x3 − 3x4 + 9x3
− + −
2x4 − 5x3 − 5x2
2x4 − x3 + 3x2
− + −
− 4x3 − 8x2 − x
− 4x3 + 2x2 − 6x
+ − +
−10x2 + 5x − 15
−10x2 + 5x − 15
+ − +
0
Since the remainder is 0,
Hence, 2x2 − x + 3 is a factor of 6x5 − x4 + 4x3 − 5x2 − x − 15
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