Question

Let $P(x)=3x^3 - 2x^2 + kx +4$. If $\frac{P(x)}{x-2}$ has remainder 12, what is the remainder of $\frac{P(x)}{x-1}$.?

Answer 1

Use the remainder theorem, which says the remainder upon dividing a polynomial $P(x)$ by $x-c$ is equal to $P(c)$.

We're told that dividing $P(x)$ by $x-2$ leaves a remainder of 12, so

$P(2)=20+2k=12\implies k=-4$

Then the remainder upon dividing by $x-1$ is $P(1)=\boxed{1}$.

Answer 2

Answer:

1

Step-by-step explanation:

Remainder theorem: f(x)/x-a = f(a)

Since we are divinding p(x) by x - 1, we can use the theorem above to help us solve.

p(x)/x-1 = p(1)

Best of Luck!