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

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

mathmate Group TitleBest ResponseYou've already chosen the best response.0
What 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.
 2 years ago

cwrw238 Group TitleBest ResponseYou've already chosen the best response.0
this is called the Remainder THEorem
 2 years ago

jhonyy9 Group TitleBest ResponseYou've already chosen the best response.1
(3x4+2x3x2+2x14) : (x+2) =3x34x2+7x12 3x4+6x3  0 4x3x2 4x38x2  0 7x2+2x 7x2+14x  0 12x14 12x24  0 10
 2 years ago

JamesJ Group TitleBest 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
 2 years ago
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