Using the remainder theorem, the value of k in f(x) = 3x^2 + kx - 7 is 10
The given parameters are:
f(x) = 3x^2 + kx - 7
Divisor = x - 4
Remainder = 81
To solve for k, we use the remainder theorem
Set the divisor to 0
x -4 = 0
Add 4 to both sides of the above equation
x - 4 + 4 = 0 + 4
This gives
x = 4
Substitute x = 4 in the function f(x) = 3x^2 + kx - 7
f(4) = 3(4)^2 + k * 4 - 7
Evaluate the exponents
f(4) = 3 * 16 + k * 4 - 7
Evaluate the products
f(4) = 48 + 4k - 7
So, we have:
f(4) = 41 + 4k
The remainder is 81.
So, we have
41 + 4k = 81
Subtract 41 from both sides
4k = 40
Divide both sides of the above equation by 4
4k/4 = 40/4
Evaluate the division
k = 10
Hence, the value of k in f(x) = 3x^2 + kx - 7 is 10 using the remainder theorem
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