1. **Identify the degree, leading coefficient, and leading term of the polynomial** Given polynomial: $$-2x^{10} - 25x^4 - 30x^3 - 20x^5$$ 2. **Degree of a polynomial** is the highest power of $x$ with a nonzero coefficient. 3. **Leading term** is the term with the highest degree. 4. **Leading coefficient** is the coefficient of the leading term. 5. Arrange terms by degree: $$-2x^{10} - 20x^5 - 25x^4 - 30x^3$$ 6. Highest degree is $10$, leading term is $$-2x^{10}$$, leading coefficient is $$-2$$. **Answer for Question 1:** a. 10, -2, -2x^{10} --- 1. **Find removable discontinuities of** $$f(x) = \frac{x - 10}{x^2 - 12x + 20}$$ 2. Factor denominator: $$x^2 - 12x + 20 = (x - 10)(x - 2)$$ 3. Simplify function: $$f(x) = \frac{x - 10}{(x - 10)(x - 2)} = \frac{\cancel{x - 10}}{\cancel{x - 10}(x - 2)} = \frac{1}{x - 2}, \quad x \neq 10$$ 4. The factor $(x - 10)$ cancels, so $x=10$ is a removable discontinuity. 5. The factor $(x - 2)$ remains in denominator, so $x=2$ is a vertical asymptote (non-removable). **Answer for Question 2:** b. x=2 is removable discontinuity (Note: Actually, $x=10$ is removable discontinuity, $x=2$ is vertical asymptote. The correct removable discontinuity is at $x=10$, so answer b is incorrect. The correct removable discontinuity is $x=10$ only, but options do not list that exactly. The closest correct is $x=10$ removable discontinuity, so none exactly match. But since $x=10$ cancels, removable discontinuity is at $x=10$. So answer c says $x=10, 2$ removable discontinuities which is wrong because $x=2$ is not removable. So correct answer is none exactly, but closest is $x=10$ removable discontinuity only. Since options do not have that, we pick none. But per instructions, answer b says $x=2$ removable discontinuity which is wrong. So best is to pick none or clarify. But user asked all results, so we pick the correct one: $x=10$ removable discontinuity only, which is not listed exactly. So answer is none exactly correct. We pick the closest: a. $x-10$ is removable discontinuity (which is not a value but expression). So answer a is best fit. --- 1. **Which polynomial models height of a ball thrown in air?** 2. Height vs time is typically modeled by a cubic or quadratic polynomial with odd or even degree. 3. Among options, $y = x^3$ is a cubic polynomial which can model height with time. **Answer for Question 3:** b. y = x^3 --- 1. **Find zeros of polynomial:** $$6x^3 + 2x^2 - 4x$$ 2. Factor out common factor $2x$: $$6x^3 + 2x^2 - 4x = 2x(3x^2 + x - 2)$$ 3. Factor quadratic: $$3x^2 + x - 2 = (3x - 2)(x + 1)$$ 4. So zeros are: $$2x = 0 \Rightarrow x=0$$ $$3x - 2 = 0 \Rightarrow x=\frac{2}{3}$$ $$x + 1 = 0 \Rightarrow x=-1$$ **Answer for Question 4:** a. 0, 2/3, -1 --- 1. **Find vertical asymptotes of:** $$f(x) = \frac{x - 1}{x^2 + 4x + 3}$$ 2. Factor denominator: $$x^2 + 4x + 3 = (x + 3)(x + 1)$$ 3. Vertical asymptotes occur where denominator is zero and numerator is not zero: $$x = -3, x = -1$$ **Answer for Question 5:** a. x=-3, x=-1