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Given f(x)= 2x^2+kx+9, and the remainder when f(x) is divided by x-4 is 81, then what is the value of k?

User LouieC
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1 Answer

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The Remainder Theorem states that if a polynomial f(x) is divided by (x - c), then the remainder is f(c). This means that if the polynomial f(x) = 2x^2 + kx + 9 is divided by (x - 4) and the remainder is 81, then we can find the value of k by setting f(4) equal to 81 and solving for k.

So:

f(4) = 81

2(4)^2 + k(4) + 9 = 81

2(16) + 4k + 9 = 81

32 + 4k + 9 = 81

4k + 41 = 81

4k = 81 - 41

4k = 40

k = 40 / 4

k = 10

So, the value of k is 10.

User Jeremy Karlsson
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