Question - Finding the Remainder of a Polynomial Using the Remainder Theorem
mathdividing polynomialspolynomial remainder theoremfind remainder polynomialremainder when dividing polynomials
Solution:
To find the remainder of the polynomial $$-x^3 + x^2 + 5x - 6$$ when divided by $$x + 3$$, you can use the Remainder Theorem. According to this theorem, if a polynomial $$f(x)$$ is divided by a binomial of the form $$x - c$$, the remainder is the value of $$f(c)$$.However, we have $$x + 3$$ instead of $$x - c$$, so we need to find $$f(-3)$$, because $$-3$$ is the root of the binomial $$x + 3$$.Let's calculate $$f(-3)$$:$$f(-3) = -(-3)^3 + (-3)^2 + 5(-3) - 6$$$$f(-3) = -(-27) + 9 - 15 - 6$$$$f(-3) = 27 + 9 - 15 - 6$$$$f(-3) = 36 - 21$$$$f(-3) = 15$$So, the remainder when $$-x^3 + x^2 + 5x - 6$$ is divided by $$x + 3$$ is $$15$$.The correct answer is (B) 15.
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