Find the remainder of f(x) divided by x^2 - 1 when f(x) = x^10 - 8x^8+7x^4+ 8x^3-12x^2 -15x - 5.
As before, use the onilne calculator, here is the answer:
And an image of the solution:
The fractional expression is the last term in this, so the remainder is -7x -17.
No, there is no need to use a calculator for this problem.
f(x) = (x^2 - 1)q(x) + r(x)
We know that r(x) is a linear equation in the form of ax + b.
f(1) = -24 = a + b (The first term cancels out)
f(-1) = -10 = -a + b
Therefore, we get two system of equations.
a + b = -24
-a + b = -10
b = -17
a = -7
Hence, the remainder is -7x - 17.