Polynomial and rational functions Knowledge-Based Practice

Math · Functions & Trigonometry · Math · Polynomial, Radical & Rational Functions

5 Math practice questions on Polynomial and rational functions. Questions that assess core concepts and understanding.

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Questions

1.
When the polynomial $P(x) = 2x^3 - kx^2 + 5x - 6$ is divided by $x - 2$ , the remainder is twice the remainder obtained when $P(x)$ is divided by $x + 1$ . What is the value of $k$ ?
- A) 11
- B) 23
- C) -11
- D) -23
2.
A polynomial function $P(x)$ with real coefficients has degree 4, a leading coefficient of 1, and zeros at $x = 3$ with multiplicity 2 and at $x = -2i$ . What is the value of $P(1)$ ?
- A) 10
- B) 16
- C) 20
- D) 36
3.
At what point does the graph of the rational function $f(x) = \frac{2x^2 + 3x - 5}{x^2 - 4}$ intersect its horizontal asymptote?
- A) $(1, 2)$
- B) $(-1, 0)$
- C) $(-1, 2)$
- D) $(-3, 2)$
4.
Which statement correctly describes the discontinuities of the rational function $f(x) = \frac{2x^2 - 2}{x^2 + 2x - 3}$ ?
- A) Vertical asymptote at $x = 1$ and removable discontinuity at $x = -3$
- B) Vertical asymptotes at both $x = 1$ and $x = -3$
- C) Removable discontinuity at $x = 1$ and vertical asymptote at $x = -3$
- D) Removable discontinuities at both $x = 1$ and $x = -3$
5.
What is the equation of the slant (oblique) asymptote of the rational function $f(x) = \frac{3x^2 - 4x + 5}{x - 1}$ ?
- A) $y = 3x + 1$
- B) $y = 3x - 4$
- C) $y = 3x - 1$
- D) $y = 3x + 2$

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