consider the polynomial functionsp given by p(x) = 7x to the 3rd power - 2x to the second power +3x+10 Evluate the function at x=-3

Given the polynomial function:

\[
p(x) = 7x^3 - 2x^2 + 3x + 10
\]

We want to evaluate the function at \(x = -3\).

Substitute \(x = -3\) into the polynomial:

\[
p(-3) = 7(-3)^3 - 2(-3)^2 + 3(-3) + 10
\]

Now calculate each term step by step:

1. \((-3)^3 = -27\), so \(7(-3)^3 = 7 \times -27 = -189\)
2. \((-3)^2 = 9\), so \(-2(-3)^2 = -2 \times 9 = -18\)
3. \(3(-3) = 3 \times -3 = -9\)
4. The constant term is \(10\)

Now sum up all the terms:

\[
p(-3) = -189 - 18 - 9 + 10
\]
\[
p(-3) = -206
\]

Thus, \(p(-3) = -206\).

Would you like further details or have any questions?

Here are 5 related questions for deeper exploration:
1. What is the degree of the polynomial function \(p(x)\)?
2. How do you find the roots of the polynomial function \(p(x)\)?
3. What is the derivative of \(p(x)\)?
4. Can you factor the polynomial \(p(x)\)?
5. What is the behavior of \(p(x)\) as \(x\) approaches infinity?

**Tip:** When substituting negative numbers into polynomial functions, be careful with the signs, especially with powers of negative numbers.

consider the polynomial function p given by p(x) = 7x to the 3rd power - 2x to the second power + 3x + 10. Evaluate the function at x=-3

Learn how to evaluate the polynomial function p(x) = 7x^3 - 2x^2 + 3x + 10 at x = -3. This solution covers key algebraic concepts and polynomial function evaluation, with a detailed step-by-step solution. Suitable for students in Grades 9-12.

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