Question

Given f(x)=3x^2+kx-7 and the remainder when f(x) is divided by x-4 is 81, then what is the value of k

Answer 1

Using the remainder theorem, the value of k in f(x) = 3x^2 + kx - 7 is 10

How to solve for k?

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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