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Let's solve the problem where we need to match each standard form polynomial to its correct factored form.

1. **\( 6x^2 - 21x \)**:
   - Factor out the common term \( 3x \):
   \[
   6x^2 - 21x = 3x(2x - 7)
   \]
   Match: **\( 3x(2x - 7) \)**

2. **\( 3x^2 - 2x - 5 \)**:
   - Factor using the quadratic factoring technique or trial-and-error:
   \[
   3x^2 - 2x - 5 = (3x + 2)(x - 4)
   \]
   Match: **\( (3x + 2)(x - 4) \)**

3. **\( x^2 + 2x - 15 \)**:
   - Factor the quadratic:
   \[
   x^2 + 2x - 15 = (x + 5)(x - 3)
   \]
   Match: **\( (x + 5)(x - 3) \)**

4. **\( 16x^2 - 25 \)**:
   - This is a difference of squares:
   \[
   16x^2 - 25 = (4x + 5)(4x - 5)
   \]
   Match: **\( (4x + 5)(4x - 5) \)**

5. **\( 3x^2 - 10x - 8 \)**:
   - Factor the quadratic:
   \[
   3x^2 - 10x - 8 = (3x - 5)(x + 1)
   \]
   Match: **\( (3x - 5)(x + 1) \)**

6. **\( 10x^2 + 15x \)**:
   - Factor out the common term \( 5x \):
   \[
   10x^2 + 15x = 5x(2x + 3)
   \]
   Match: **\( 5x(2x + 3) \)**

Here’s the complete matching:

- \( 6x^2 - 21x \) ↔ \( 3x(2x - 7) \)
- \( 3x^2 - 2x - 5 \) ↔ \( (3x + 2)(x - 4) \)
- \( x^2 + 2x - 15 \) ↔ \( (x + 5)(x - 3) \)
- \( 16x^2 - 25 \) ↔ \( (4x + 5)(4x - 5) \)
- \( 3x^2 - 10x - 8 \) ↔ \( (3x - 5)(x + 1) \)
- \( 10x^2 + 15x \) ↔ \( 5x(2x + 3) \)

Would you like further details on any of these steps or have any other questions?

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Here are 5 related questions:
1. How do you factor a quadratic expression?
2. What is the difference of squares and how is it factored?
3. How do you identify common factors in polynomials?
4. What is the quadratic formula and when is it used?
5. Can you always factor a quadratic expression?

**Tip:** Always look for common factors before applying any other factoring technique!

Match each standard form card to the correct factored form.

This problem covers matching polynomials in standard form to their corresponding factored form. It includes concepts such as quadratic factoring, difference of squares, and factoring out the greatest common factor. Suitable for students in Grades 8-10.

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