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Factor Remainder Theorem?
Given that x^5 - 2x^4 + 2x^3 - 4x^2 - 3x + 6 is exactly divisible by x^2 + 3
find the remaining real factors of the polynomial.
3 Answers
- Your AnswerLv 61 decade ago
x^5 - 2x^4 + 2x^3 - 4x^2 - 3x + 6 is exactly divisible by x^2 + 3
then x^5 - 2x^4 + 2x^3 - 4x^2 - 3x + 6
= (x^2 + 3)(x^3 -- 2x^2 -- x + 2)
= (x^2 + 3)(x -- 2)(x^2 -- 1)
= (x^2 + 3)(x -- 2)(x + 1)(x --1)
- An ESL LearnerLv 71 decade ago
.........................................x^3 - 2x^2 - x + 2
..................____________________________
x^2 + 0x + 3)x^5 - 2x^4 + 2x^3 - 4x^2 - 3x + 6
...................x^5 + 0x^4 + 3x^3
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.............................-2x^4 - x^3 - 4x^2
.............................-2x^4 - 0x^3 - 6x^2
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.....................................-x^3 + 2x^2 - 3x
.....................................-x^3 - 0x^2 - 3x
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...............................................2x^2 + 0x + 6
...............................................2x^2 + 0x + 6
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∴ the remaining real factors of the polynomial is x^3 - 2x^2 - x + 2 or (x + 1)(x - 1)(x - 2)
