the zeros of a cubic function are -2,3, and 4/3 give the factors of the function

To find the factors of a cubic function given its zeros, we can use the fact that if \( x = a \), then \( (x - a) \) is a factor of the function.

Given the zeros \( -2 \), \( 3 \), and \( \frac{4}{3} \), the factors of the cubic function are:

\[
(x + 2), (x - 3), \left( x - \frac{4}{3} \right)
\]

To express the function in a simpler form, we can eliminate the fraction in the third factor by multiplying it by 3:

\[
3 \left( x - \frac{4}{3} \right) = (3x - 4)
\]

Thus, the factors of the function are:

\[
(x + 2), (x - 3), (3x - 4)
\]

So, the cubic function in factored form is:

\[
f(x) = (x + 2)(x - 3)(3x - 4)
\]

Would you like further details, or do you have any questions?

Here are 5 related questions:
1. How can we expand the cubic function from its factored form?
2. What does the graph of this cubic function look like?
3. How do you determine the multiplicity of the zeros in a cubic function?
4. How do transformations affect the graph of a cubic function?
5. What is the relationship between the coefficients of a cubic function and its zeros?

**Tip**: When finding the zeros of a function, remember that each zero corresponds to a factor of the form \( (x - a) \), where \( a \) is the zero.

The zeros of a cubic function are -2, 3, and 4/3. Give the factors of the function.

Learn how to find the factors of a cubic function with zeros at -2, 3, and 4/3. This algebra problem covers factoring polynomials and using the factor theorem, suitable for students in Grades 9-12.

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