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mcshweezy
 3 years ago
What is the remainder when (3x4 + 2x3 – x2 + 2x – 14) ÷ (x + 2) ?
mcshweezy
 3 years ago
What is the remainder when (3x4 + 2x3 – x2 + 2x – 14) ÷ (x + 2) ?

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JamesJ
 3 years ago
Best ResponseYou've already chosen the best response.1@hoblos: if you answer it, you explain it!

mathmate
 3 years ago
Best ResponseYou've already chosen the best response.0What you do is to evaluate the numerator, using x=2 (from x+2=0), and what you get is the remainder, namely 10 as Hoblos posted.

cwrw238
 3 years ago
Best ResponseYou've already chosen the best response.0this is called the Remainder THEorem

jhonyy9
 3 years ago
Best ResponseYou've already chosen the best response.2(3x4+2x3x2+2x14) : (x+2) =3x34x2+7x12 3x4+6x3  0 4x3x2 4x38x2  0 7x2+2x 7x2+14x  0 12x14 12x24  0 10

JamesJ
 3 years ago
Best ResponseYou've already chosen the best response.1@cwrw: right. The idea is that given any polynomial p(x) and a linear term such as (x+2), then we write p(x) as p(x) = (x+2)q(x) + r  (*) where q(x) is another polynomial. r is the remainder after p(x) is divided by (x+2). ===== If x=2 is a root of the polynomial p(x), then p(2) = 0. Hence using equation (*), 0 = p(2) = (2+2)q(2) + r = 0 + r i.e., r = 0. If x=2 is not a root of p(x), then r will not be zero. It can be calculated by evaluating p(2), because p(2) = (2+2)q(2) + r = 0 + r i.e., r = p(2) ===== So this is why a shortcut way to finding the remainder of p(x) = 3x^4 + 2x^3 – x^2 + 2x – 14 when divided by (x+2) is just to evaluate p(x) for x = 2: r = p(2) = 3(2)^4 + 2(2)^3  (2)^2 + 2(2)  14 = 48  16  4  4  14 = 10

malice
 3 months ago
Best ResponseYou've already chosen the best response.0The answer is *not* ten, just took the test

mathmate
 3 months ago
Best ResponseYou've already chosen the best response.0@malice If the answer is *not* ten, it could be one of the many possibilities: 1. the test has an incorrect answer 2. the test question is different from what was posted above (typo, or the test is automorphic, i.e. changes the data every time the question is displayed) 3. All three or four people who responded to the question made the same mistake with probability < \(0.01^4=10^{8}\). Actually this is an excellent lesson to learn: We do not take answers from someone else and use it as our own work (plagiarism). Work out the problem personally so that we know HOW to do the work. Finally, you also realize that getting \(help\) or answers from this site or anywhere else for an online test is considered cheating, and is taken very seriously by the authorities.
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