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The expression provided is \((1 + x)(x^2 - 5x - 6)\).

To find the polynomial in standard form, we need to expand the expression using the distributive property.

\[
(1 + x)(x^2 - 5x - 6) = 1 \cdot (x^2 - 5x - 6) + x \cdot (x^2 - 5x - 6)
\]

Let's compute each term separately:

1. \( 1 \cdot (x^2 - 5x - 6) = x^2 - 5x - 6 \)
2. \( x \cdot (x^2 - 5x - 6) = x^3 - 5x^2 - 6x \)

Now, add both results together:

\[
x^2 - 5x - 6 + x^3 - 5x^2 - 6x
\]

Combine like terms:

\[
x^3 - 4x^2 - 11x - 6
\]

So, the polynomial in standard form is:

\[
x^3 - 4x^2 - 11x - 6
\]

Would you like further clarification on any part of this process?

Here are five follow-up questions to deepen your understanding:
1. What is the distributive property, and how does it apply in polynomial multiplication?
2. How do you identify and combine like terms in a polynomial?
3. What is the degree of the polynomial \(x^3 - 4x^2 - 11x - 6\)?
4. How would you factor the polynomial \(x^3 - 4x^2 - 11x - 6\), if possible?
5. How does multiplying a binomial by a trinomial differ from multiplying two binomials?

**Tip:** When expanding polynomials, always distribute each term of the first expression to every term of the second one, and then combine like terms to simplify.

Learn how to expand and simplify the polynomial expression (1 + x)(x^2 - 5x - 6) using the distributive property. This step-by-step solution explains the process of multiplying a binomial by a trinomial, simplifying it to x^3 - 4x^2 - 11x - 6.

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