Answered

Lorne subtracted [tex]$6x^3 - 2x + 3$[/tex] from [tex]-3x^3 + 5x^2 + 4x - 7[/tex]. Use the drop-down menus to identify the steps Lorne used to find the difference.

1. [tex](-3x^3 + 5x^2 + 4x - 7) - (6x^3 - 2x + 3)[/tex]

2. [tex](-3x^3) + 5x^2 + 4x + (-7) - (6x^3 - 2x + 3)[/tex]

3. [tex][(-3x^3) - 6x^3] + [4x - (-2x)] + [(-7) - 3] + [5x^2][/tex]

4. [tex]-9x^3 + 6x + (-10) + 5x^2[/tex]

5. [tex]-9x^3 + 5x^2 + 6x - 10[/tex]



Answer :

GinnyAnswer
Certainly! Let’s walk through the steps used by Lorne to subtract [tex]\(6x^3 - 2x + 3\)[/tex] from [tex]\(-3x^3 + 5x^2 + 4x - 7\)[/tex].

1. Step 1: Set up the subtraction problem as addition by adding the negative of the second polynomial.
[tex]\[ \left(-3x^3 + 5x^2 + 4x - 7\right) + \left(-6x^3 + 2x - 3\right) \][/tex]

2. Step 2: Clearly distribute and separate each term from the two polynomials.
[tex]\[ \left(-3x^3\right) + 5x^2 + 4x + (-7) + \left(-6x^3\right) + 2x + (-3) \][/tex]

3. Step 3: Group like terms together.
[tex]\[ \left[\left(-3x^3\right) + \left(-6x^3\right)\right] + [4x + 2x] + [(-7) + (-3)] + \left[5x^2\right] \][/tex]

4. Step 4: Simplify each group of like terms.
[tex]\[ -9x^3 + 6x + (-10) + 5x^2 \][/tex]

5. Step 5: Rewrite the final simplified polynomial.
[tex]\[ -9x^3 + 5x^2 + 6x - 10 \][/tex]

This step-by-step solution clearly illustrates how Lorne subtracted the polynomials and combined like terms to arrive at the final expression.

Other Questions