https://file.aiquickdraw.com/mathbot/file/1727000074993k2pnnoue.jpg

Let's work through the questions from the image.

1. **The first question:**
   \( f(x) = x^3 - 71x^2 - x + 71 \)
   
   We need to **factor** this cubic polynomial.

2. **The second question:**
   \( f(x) = x^3 + 23x^2 + 71x - 95 \)
   
   Here, we also need to **factor** this cubic polynomial.

Let me factor these polynomials step by step.

### First Polynomial: \( f(x) = x^3 - 71x^2 - x + 71 \)

I'll start by checking for any rational roots using the Rational Root Theorem, followed by factoring.

### Second Polynomial: \( f(x) = x^3 + 23x^2 + 71x - 95 \)

The same approach will be used for this one as well.

Let me work out the factorizations.Here are the factorizations of the given polynomials:

1. For \( f(x) = x^3 - 71x^2 - x + 71 \), the factors are:
   \[
   f(x) = (x - 71)(x - 1)(x + 1)
   \]

2. For \( f(x) = x^3 + 23x^2 + 71x - 95 \), the factors are:
   \[
   f(x) = (x - 1)(x + 5)(x + 19)
   \]

Do you have any questions or would you like further details on these factorizations?

Here are 5 related questions you might explore:
1. How does the Rational Root Theorem help in factoring polynomials?
2. What is the process of synthetic division when finding polynomial factors?
3. Can every cubic polynomial be factored into linear factors?
4. How can you confirm if a factorization is correct?
5. What are the implications of the factored form for graphing a polynomial?

**Tip:** When factoring, checking for rational roots using possible factors of the constant term and leading coefficient can simplify the process!

1. Tentukan faktor-faktor dari f(x) = x^3 - 71x^2 - x + 71
2. Carilah faktor-faktor dari f(x) = x^3 + 23x^2 + 71x - 95

Learn how to factor the cubic polynomials f(x) = x^3 - 71x^2 - x + 71 and f(x) = x^3 + 23x^2 + 71x - 95. This step-by-step solution explains the use of the Rational Root Theorem to find the roots and factor the expressions. Suitable for students in Grades 10-12.

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