1. The problem is to identify a polynomial that satisfies the following conditions: a. The polynomial has a degree of 4. b. It has three terms. c. One of the terms has degree 1. d. One of the terms has a coefficient of -5. e. The polynomial has a y-intercept at 10. 2. Recall that the degree of a polynomial is the highest power of $x$ in the expression. 3. Since the polynomial has degree 4 and three terms, it can be written as: $$ax^4 + bx + c$$ where $a$, $b$, and $c$ are coefficients, and $bx$ is the term with degree 1. 4. One of the coefficients is -5, so either $a = -5$, $b = -5$, or $c = -5$. 5. The y-intercept is the value of the polynomial when $x=0$, which equals $c$. Given the y-intercept is 10, we have: $$c = 10$$ 6. Since $c = 10$, the coefficient -5 must be either $a$ or $b$. 7. The polynomial can be: $$-5x^4 + bx + 10$$ or $$ax^4 - 5x + 10$$ 8. Both satisfy the conditions: degree 4, three terms, one term degree 1, one coefficient -5, and y-intercept 10. Final answer: The polynomial is either $$-5x^4 + bx + 10$$ or $$ax^4 - 5x + 10$$ where $a$ and $b$ are any real numbers except zero to maintain the degree and terms.