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The expression to factor is:

\[
3x^2 - 14x + 15
\]

To factor this quadratic trinomial, we'll use the method of grouping. First, we need to find two numbers that multiply to \( 3 \times 15 = 45 \) and add up to \(-14\).

The two numbers are \(-5\) and \(-9\) because:

\[
-5 \times -9 = 45 \quad \text{and} \quad -5 + (-9) = -14
\]

Now, rewrite the middle term using these two numbers:

\[
3x^2 - 5x - 9x + 15
\]

Next, group the terms:

\[
(3x^2 - 5x) - (9x - 15)
\]

Factor out the greatest common factor from each group:

\[
x(3x - 5) - 3(3x - 5)
\]

Now, factor out the common binomial factor \((3x - 5)\):

\[
(3x - 5)(x - 3)
\]

So, the factored form of \(3x^2 - 14x + 15\) is:

\[
(3x - 5)(x - 3)
\]

Would you like more details on this process or have any questions?

Here are some related questions you might find helpful:

1. How do you factor quadratic trinomials in general?
2. What is the method of grouping, and when is it used?
3. Can all quadratic equations be factored using integers?
4. How do you solve a quadratic equation after factoring?
5. What is the significance of the coefficients in a quadratic expression?

**Tip:** When factoring trinomials, always check if the quadratic can be factored using simple methods like grouping or trial and error before resorting to more complex techniques.

Learn how to factor the quadratic expression 3x^2 - 14x + 15 using the grouping method. This tutorial breaks down the steps and explains key concepts in algebra, perfect for students in Grades 9-12.

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