If f, left bracket, x, right bracket, equals, 5, x, cubed, plus, x, minus, 2f(x)=5x 3 +x−2, then what is the remainder when f, left bracket, x, right bracketf(x) is divided by x, plus, 1x+1?
Question
If f, left bracket, x, right bracket, equals, 5, x, cubed, plus, x, minus, 2f(x)=5x 3 +x−2, then what is the remainder when f, left bracket, x, right bracketf(x) is divided by x, plus, 1x+1?
Solution
To find the remainder when f(x) is divided by x+1, we can use the Remainder Theorem. The Remainder Theorem states that the remainder when a polynomial f(x) is divided by (x - a) is equal to f(a).
In this case, we are dividing by (x + 1), so we can rewrite this as (x - (-1)).
Therefore, to find the remainder, we substitute x = -1 into the function f(x):
f(-1) = 5(-1)^3 + (-1) - 2 = -5 - 1 - 2 = -8
So, the remainder when f(x) is divided by x+1 is -8.
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