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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 :

To solve the problem of dividing [tex]\(42x^3 - 21x^2 + 49x\)[/tex] by [tex]\(7x\)[/tex], follow these steps:

1. Divide Each Term:
- Divide the first term of the polynomial by [tex]\(7x\)[/tex].
- [tex]\(\frac{42x^3}{7x} = 6x^2\)[/tex].

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

- Divide the third term by [tex]\(7x\)[/tex].
- [tex]\(\frac{49x}{7x} = 7\)[/tex].

2. Combine the Results:
- Combine all the results from the division:
- [tex]\(6x^2 - 3x + 7\)[/tex].

So, the quotient of [tex]\( \frac{42x^3 - 21x^2 + 49x}{7x} \)[/tex] is [tex]\(6x^2 - 3x + 7\)[/tex].

The correct answer is [tex]\(6x^2 - 3x + 7\)[/tex] which matches the option [tex]\( \boxed{6x^2 - 3x + 7} \)[/tex].

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