Polynomial and rational functions Knowledge-Based Download PDF

Questions

1. 1.

   When a polynomial $P(x)$ is divided by $x - 3$, the remainder is 7, and when it is divided by $x + 2$, the remainder is $-8$. What is the remainder when $P(x)$ is divided by $(x - 3)(x + 2)$?

   • A) $2x + 1$
   • B) $3x + 2$
   • C) $-3x + 16$
   • D) $3x - 2$
2. 2.

   Given that $2 - i$ is a zero of the polynomial function $P(x) = x^3 - 6x^2 + 13x - 10$ with real coefficients, what is the real zero of $P(x)$?

   • A) $x = 2$
   • B) $x = -2$
   • C) $x = 5$
   • D) $x = -5$
3. 3.

   At what point does the graph of the rational function $f(x) = \frac{3x^2 - 4x + 5}{x^2 - 2x + 3}$ intersect its horizontal asymptote?

   • A) $(-2, 3)$
   • B) $(2, 3)$
   • C) $(2, 0)$
   • D) $(1, 3)$
4. 4.

   What are the coordinates of the removable discontinuity (hole) on the graph of the rational function $f(x) = \frac{x^2 - 9}{2x^2 + 5x - 3}$?

   • A) $(3, 0)$
   • B) $(-3, 0)$
   • C) $\left(-3, \frac{6}{7}\right)$
   • D) $\left(\frac{1}{2}, \frac{6}{7}\right)$
5. 5.

   What is the equation of the slant asymptote of the rational function $f(x) = \frac{3x^2 - 5x + 4}{x - 2}$?

   • A) $y = 3x + 1$
   • B) $y = 3x - 1$
   • C) $y = 3x - 11$
   • D) $y = 3x + 6$