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What is the remainder of this simplified rational expression?

label Algebra
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x^3+4x+5 / x+3

Oct 21st, 2017

Using the remainder theorem:

The Remainder Theorem is useful for evaluating polynomials at a given value of x, though it might not seem so, at least at first blush. This is because the tool is presented as a theorem with a proof, and you probably don't feel ready for proofs at this stage in your studies. Fortunately, you don't "have" to understand the proof of the Theorem; you just need to understand how to use the Theorem.

The Remainder Theorem starts with an unnamed polynomial p(x), where "p(x)" just means "some polynomial p whose variable is x". Then the Theorem talks about dividing that polynomial by some linear factorxa, whereais just some number.

Here, we have x + 3 = 0 ,

x = -3

Hence we will put the value of x = -3 in numerator, which will give us remainder.

x^3+4x+5

= (-3)^3 + 4(-3) + 5

= -27 - 12 + 5

= -34........................Answer.

Apr 5th, 2015

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