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Divide [tex]$42x^3 - 21x^2 + 49x$[/tex] by [tex]$7x$[/tex].

A. [tex]$6x^3 - 3x + 7$[/tex]

B. [tex]$6x^3 + 3x - 7$[/tex]

C. [tex]$6x^2 - 3x + 7$[/tex]

D. [tex]$6x^2 + 3x - 7$[/tex]

Answer :

Sure! Let's go through the steps of dividing the expression [tex]\(42x^3 - 21x^2 + 49x\)[/tex] by [tex]\(7x\)[/tex].

### Step 1: Understand the Division
We are dividing the polynomial [tex]\(42x^3 - 21x^2 + 49x\)[/tex] by [tex]\(7x\)[/tex]. This means we will divide each term of the polynomial by [tex]\(7x\)[/tex].

### Step 2: Divide Each Term
- First Term: [tex]\(42x^3\)[/tex]

Divide [tex]\(42x^3\)[/tex] by [tex]\(7x\)[/tex]:
[tex]\[
\frac{42x^3}{7x} = 6x^2
\][/tex]

- Second Term: [tex]\(-21x^2\)[/tex]

Divide [tex]\(-21x^2\)[/tex] by [tex]\(7x\)[/tex]:
[tex]\[
\frac{-21x^2}{7x} = -3x
\][/tex]

- Third Term: [tex]\(49x\)[/tex]

Divide [tex]\(49x\)[/tex] by [tex]\(7x\)[/tex]:
[tex]\[
\frac{49x}{7x} = 7
\][/tex]

### Step 3: Combine the Results
After performing the division for each term, we have:

[tex]\[
6x^2 - 3x + 7
\][/tex]

Thus, the expression [tex]\(42x^3 - 21x^2 + 49x\)[/tex] divided by [tex]\(7x\)[/tex] results in:

[tex]\[
6x^2 - 3x + 7
\][/tex]

So, the correct answer is [tex]\(6x^2 - 3x + 7\)[/tex].

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