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fill it in the way that is shown in the image

To factor the quadratic expression \( 6x^2 - 7x + 2 \), we need to find two binomials that multiply to give this expression.

The expression is factored in the form:
\[
(2x - ?)(3x - ?)
\]

### Step-by-step solution:

1. **First term:**
   The first term is \( 6x^2 \). To get this, we must have factors \( 2x \) and \( 3x \) in the two binomials, since \( 2x \times 3x = 6x^2 \).

2. **Last term:**
   The last term in the quadratic is \( +2 \). We need two numbers that multiply to \( 2 \). The possible pairs are \( (1, 2) \) or \( (-1, -2) \).

3. **Middle term:**
   The middle term is \( -7x \), which comes from adding the products of the inner and outer terms when multiplying the binomials. Specifically, we need the terms that satisfy:
   \[
   2x \times (-b) + 3x \times (-a) = -7x
   \]
   Using the factor pair \( (-1, -2) \) works because:
   \[
   (2x)(-2) + (3x)(-1) = -4x - 3x = -7x
   \]

### Final factorization:
\[
(2x - 1)(3x - 2)
\]

So, the missing values in the binomials are \(1\) and \(2\), and the complete factorization is:
\[
(2x - 1)(3x - 2)
\]

Would you like more details on how to verify this factorization or have any further questions?

Here are 5 related questions to explore:
1. How do you verify if a factorization is correct?
2. Can you factor quadratics where the leading coefficient is not 1?
3. What methods can you use if the quadratic doesn’t factor easily?
4. How would you factor \( 6x^2 + 7x + 2 \) instead?
5. What is the significance of the middle term in factoring?

**Tip:** Always check your factorization by expanding it back to see if it equals the original expression!

Factor the quadratic expression 6x^2 - 7x + 2. Fill in the missing values in the binomials: (2x - ?)(3x - ?)

Learn how to factor the quadratic equation 6x^2 - 7x + 2 step-by-step. This problem involves factoring using binomials, distributive property, and zero product property. Perfect for Grades 8-10 algebra students.

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