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Answer :
To divide the polynomial [tex]\(42x^3 - 21x^2 + 49x\)[/tex] by [tex]\(7x\)[/tex], follow these simple steps:
1. Divide Each Term Separately:
- Start by dividing each term in the polynomial by the term you are dividing by, [tex]\(7x\)[/tex].
2. Divide the First Term:
- Take the first term [tex]\(42x^3\)[/tex] and divide it by [tex]\(7x\)[/tex]:
[tex]\[
\frac{42x^3}{7x} = 6x^2
\][/tex]
3. Divide the Second Term:
- Take the second term [tex]\(-21x^2\)[/tex] and divide it by [tex]\(7x\)[/tex]:
[tex]\[
\frac{-21x^2}{7x} = -3x
\][/tex]
4. Divide the Third Term:
- Take the third term [tex]\(49x\)[/tex] and divide it by [tex]\(7x\)[/tex]:
[tex]\[
\frac{49x}{7x} = 7
\][/tex]
5. Combine All Results:
- Putting it all together, you get:
[tex]\[
6x^2 - 3x + 7
\][/tex]
Therefore, the result of dividing the given polynomial [tex]\(42x^3 - 21x^2 + 49x\)[/tex] by [tex]\(7x\)[/tex] is [tex]\(\boxed{6x^2 - 3x + 7}\)[/tex]. This matches the choice [tex]\(6 x^2-3 x+7\)[/tex].
1. Divide Each Term Separately:
- Start by dividing each term in the polynomial by the term you are dividing by, [tex]\(7x\)[/tex].
2. Divide the First Term:
- Take the first term [tex]\(42x^3\)[/tex] and divide it by [tex]\(7x\)[/tex]:
[tex]\[
\frac{42x^3}{7x} = 6x^2
\][/tex]
3. Divide the Second Term:
- Take the second term [tex]\(-21x^2\)[/tex] and divide it by [tex]\(7x\)[/tex]:
[tex]\[
\frac{-21x^2}{7x} = -3x
\][/tex]
4. Divide the Third Term:
- Take the third term [tex]\(49x\)[/tex] and divide it by [tex]\(7x\)[/tex]:
[tex]\[
\frac{49x}{7x} = 7
\][/tex]
5. Combine All Results:
- Putting it all together, you get:
[tex]\[
6x^2 - 3x + 7
\][/tex]
Therefore, the result of dividing the given polynomial [tex]\(42x^3 - 21x^2 + 49x\)[/tex] by [tex]\(7x\)[/tex] is [tex]\(\boxed{6x^2 - 3x + 7}\)[/tex]. This matches the choice [tex]\(6 x^2-3 x+7\)[/tex].
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