https://file.aiquickdraw.com/mathbot/file/1729596221899o8yhp995.jpg

In this image, the problem is asking to evaluate \( p(5) \), where the polynomial function \( p(x) = x^3 + 7x^2 - 20x - 110 \) is given. We can use synthetic or direct substitution to calculate \( p(5) \).

Given that the long division in the image shows the polynomial being divided by \( (x - 5) \), we can conclude that \( x = 5 \) is a root of the polynomial. This means \( p(5) = 0 \).

Therefore, \( p(5) = 0 \).

Would you like more details on how to perform synthetic division or further explanation of polynomial evaluation?

Here are 5 related questions to deepen understanding:

1. How does synthetic division differ from long division for polynomials?
2. Why does the remainder of the division indicate the value of \( p(5) \)?
3. What does it mean if a number is a root of a polynomial function?
4. How can we factor polynomials after finding a root?
5. How do we use the remainder theorem to evaluate polynomial functions?

**Tip:** The remainder theorem states that the remainder when a polynomial \( p(x) \) is divided by \( (x - a) \) is \( p(a) \).

What is p(5) for the polynomial function p(x) = x^3 + 7x^2 - 20x - 110?

Learn how to evaluate p(5) for the polynomial function p(x) = x^3 + 7x^2 - 20x - 110 using polynomial division and the remainder theorem. This example demonstrates key algebraic concepts for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation