When a polynomial $P(x)$ is divided by $(x - a)$, and the remainder is $R$, which of the following statements is true?
Question 2
If a polynomial $P(x)$ has a root $x = a$ with multiplicity $m$, which of the following statements is true about the derivatives of $P(x)$ at $x = a$?
Question 3
Consider the polynomial $P(x) = x^3 - 7x^2 + 14x - 8$. Given that $x = 1$ is a root, what is the quadratic factor that remains after dividing $P(x)$ by $(x - 1)$?
Question 4
If a polynomial $P(x)$ has roots $x = 2$ (multiplicity 1) and $x = -1$ (multiplicity 2), which of the following could be the polynomial?
Question 5
Which of the following statements correctly describes the relationship between the roots and coefficients of a cubic polynomial $ax^3 + bx^2 + cx + d = 0$?
