Question: Consider the following polynomial function. f(x) = x^4 + x^3 - 7x^2 - 5x + 10 Step 2 of 4: Find…

Consider the following polynomial function.

f(x) = x^4 + x^3 - 7x^2 - 5x + 10

Step 2 of 4: Find the degree and the y-intercept. Express the intercept as an ordered pair.

Degree:

y-intercept:

Solution

To find the degree of the polynomial: The degree of a polynomial is the highest power of \( x \). The given polynomial is: \[ f(x) = x^4 + x^3 - 7x^2 - 5x + 10 \] The highest power of \( x \) in \( f(x) \) is 4. Therefore, the degree of the polynomial is 4. To find the y-intercept: The y-intercept occurs when \( x = 0 \). Substitute \( x = 0 \) into \( f(x) \): \[ f(0) = 0^4 + 0^3 - 7 \cdot 0^2 - 5 \cdot 0 + 10 = 10 \] Thus, the y-intercept is \( (0, 10) \). Answers: Degree: 4 y-intercept: \( (0, 10) \)