Question

lorne subtracted (6x^3 - 2x + 3) from (-3x^3 + 5x^2 + 4x - 7). use the drop-down menus to identify the steps lorne used to find the difference.

1. ((-3x^3 + 5x^2 + 4x - 7) + (-6x^3 + 2x - 3))
2. ((-3x^3) + 5x^2 + 4x + (-7) + (-6x^3) + 2x + (-3))
3. ((-3x^3) + (-6x^3) + 4x + 2x + (-7) + (-3) + 5x^2)
4. (-9x^3 + 6x + (-10) + 5x^2)
5. (-9x^3 + 5x^2 + 6x - 10)

options:
combined like terms
grouped like terms
wrote as addition of the additive inverse
wrote terms as addition of opposite

Explanation:

Analyze Step 1

$$ (-3x^3 + 5x^2 + 4x - 7) - (6x^3 - 2x + 3) = (-3x^3 + 5x^2 + 4x - 7) + (-6x^3 + 2x - 3) $$

This step rewrites subtraction as addition of the additive inverse.

Analyze Step 2

$$ (-3x^3) + 5x^2 + 4x + (-7) + (-6x^3) + 2x + (-3) $$

This step rewrites subtraction of terms within each polynomial as addition of their opposites.

Analyze Step 3 and Step 4

$$ \text{Step 3: } [(-3x^3) + (-6x^3)] + [4x + 2x] + [(-7) + (-3)] + [5x^2] \implies \text{grouped like terms} $$

$$ \text{Step 4: } -9x^3 + 6x + (-10) + 5x^2 \implies \text{combined like terms} $$

Answer:

Step	Description
Step 2	wrote terms as addition of opposite
Step 3	grouped like terms
Step 4	combined like terms