SOLUTION: Determine the values of b so that when f(x) is divided by (x-2) the remainder is -2:
1. f(x)= x^3-bx^2+4x-20
2. f(x)= -2x^4+40x^2-24x+b
3. f(x)= x^3-2bx^2+3x-4
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Polynomials-and-rational-expressions
-> SOLUTION: Determine the values of b so that when f(x) is divided by (x-2) the remainder is -2:
1. f(x)= x^3-bx^2+4x-20
2. f(x)= -2x^4+40x^2-24x+b
3. f(x)= x^3-2bx^2+3x-4
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Question 1092470: Determine the values of b so that when f(x) is divided by (x-2) the remainder is -2:
1. f(x)= x^3-bx^2+4x-20
2. f(x)= -2x^4+40x^2-24x+b
3. f(x)= x^3-2bx^2+3x-4 Found 2 solutions by Edwin McCravy, ikleyn:Answer by Edwin McCravy(20060) (Show Source):
2 | 1 -b 4 -20
| 2 4-2b 16-4b
1 2-b 8-2b -4-4b
The remainder is -4-4b and it must equal to -2,
so we set the remainder equal to -2:
-4-4b = -2
+4 +4
----------
-4b = 2
b =
Edwin
Apply the Remainder theorem.
The remainder theorem says that
if a polynomial f(x) is divided by a binomial (x-a), where "a" is a constant term (a number),
then the remainder is equal to the value of f(x) at x= a, i.e. f(a).
In your case a = 2. By y substituting x= 2 into f(x) you get
f(2) = 2^3 -b*2^2 + 4*2 - 20 = 8 - 4b + 8 - 20 = -4b - 4.
Therefore, your equation to find "b" is
-4b - 4 = -2 (since -2 is the remainder !)
which implies 4b = 2 - 4 = -2, b = = -0.5.
