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 factorx–a, 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.
= (-3)^3 + 4(-3) + 5
= -27 - 12 + 5
Apr 5th, 2015
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