Lorne subtracted 6*x*3 – 2*x* + 3 from –3*x*3 + 5*x*2 + 4*x* – 7. Use the drop-down menus to identify the steps Lorne used to find the difference.

1. (–3*x*3 + 5*x*2 + 4*x* – 7) + (–6*x*3 + 2*x* – 3)

combined like termsgrouped like termswrote as addition of the additive inversewrote terms as addition of opposite

2. (–3*x*3) + 5*x*2 + 4*x* + (–7) + (–6*x*3) + 2*x* + (–3)

combined like termsgrouped like termswrote as addition of the additive inversewrote terms as addition of opposite

3. [(–3*x*3) + (–6*x*3)] + [4*x* + 2*x*] + [(–7) + (–3)] + [5*x*2]

combined like termsgrouped like termswrote as addition of the additive inversewrote terms as addition of opposite

4. –9*x*3 + 6*x* + (–10) + 5*x*2

combined like termsgrouped like termswrote as addition of the additive inversewrote terms as addition of opposite

5. –9*x*3 + 5*x*2 + 6*x* – 10 

Let's go through the steps Lorne used to find the difference step by step and identify the correct operations for each.

### Step 1:
Subtract \( 6x^3 - 2x + 3 \) from \( -3x^3 + 5x^2 + 4x - 7 \):
\[ (-3x^3 + 5x^2 + 4x - 7) - (6x^3 - 2x + 3) \]
This is equivalent to adding the additive inverse:
\[ (-3x^3 + 5x^2 + 4x - 7) + (-6x^3 + 2x - 3) \]

So, the correct choice for Step 1 is:
**wrote as addition of the additive inverse**

### Step 2:
Write the expression with grouped terms:
\[ (-3x^3) + 5x^2 + 4x + (-7) + (-6x^3) + 2x + (-3) \]

So, the correct choice for Step 2 is:
**wrote terms as addition of opposite**

### Step 3:
Group like terms:
\[ [(-3x^3) + (-6x^3)] + [4x + 2x] + [(-7) + (-3)] + [5x^2] \]

So, the correct choice for Step 3 is:
**grouped like terms**

### Step 4:
Combine like terms:
\[ -9x^3 + 6x + (-10) + 5x^2 \]

So, the correct choice for Step 4 is:
**combined like terms**

### Step 5:
Write the final expression:
\[ -9x^3 + 5x^2 + 6x - 10 \]

The steps with the correct choices are:

1. **wrote as addition of the additive inverse**
2. **wrote terms as addition of opposite**
3. **grouped like terms**
4. **combined like terms**
5. \( -9x^3 + 5x^2 + 6x - 10 \)

Would you like more details or have any questions? Here are some questions you might find interesting:

1. What are the properties of polynomial subtraction?
2. How can you verify your polynomial subtraction result?
3. What is the significance of the additive inverse in polynomial operations?
4. Can polynomial subtraction change the degree of the polynomial?
5. How do you approach polynomial subtraction with multiple variables?

**Tip:** When subtracting polynomials, always remember to distribute the negative sign to each term of the polynomial being subtracted before combining like terms.

Learn how to subtract polynomials step-by-step with an example problem. This guide covers polynomial operations, combining like terms, and using the additive inverse. Suitable for high school students.

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