Answer :
To divide the polynomial [tex]\(42x^3 - 21x^2 + 49x\)[/tex] by [tex]\(7x\)[/tex], follow these steps:
1. Divide Each Term Separately:
- Start with the first term: [tex]\(\frac{42x^3}{7x}\)[/tex].
- Divide the coefficients: [tex]\(\frac{42}{7} = 6\)[/tex].
- Subtract the exponents of [tex]\(x\)[/tex]: [tex]\(x^{3-1} = x^2\)[/tex].
- This gives us [tex]\(6x^2\)[/tex].
- Move on to the second term: [tex]\(\frac{-21x^2}{7x}\)[/tex].
- Divide the coefficients: [tex]\(\frac{-21}{7} = -3\)[/tex].
- Subtract the exponents of [tex]\(x\)[/tex]: [tex]\(x^{2-1} = x\)[/tex].
- This gives us [tex]\(-3x\)[/tex].
- Lastly, divide the third term: [tex]\(\frac{49x}{7x}\)[/tex].
- Divide the coefficients: [tex]\(\frac{49}{7} = 7\)[/tex].
- Subtract the exponents of [tex]\(x\)[/tex]: [tex]\(x^{1-1} = x^0\)[/tex], and [tex]\(x^0\)[/tex] is 1.
- This gives us [tex]\(+7\)[/tex].
2. Combine the Results:
- Combine the results from each term: [tex]\(6x^2 - 3x + 7\)[/tex].
Based on these calculations, the quotient is [tex]\(6x^2 - 3x + 7\)[/tex].
Therefore, the correct choice is:
[tex]\(6x^2 - 3x + 7\)[/tex]
1. Divide Each Term Separately:
- Start with the first term: [tex]\(\frac{42x^3}{7x}\)[/tex].
- Divide the coefficients: [tex]\(\frac{42}{7} = 6\)[/tex].
- Subtract the exponents of [tex]\(x\)[/tex]: [tex]\(x^{3-1} = x^2\)[/tex].
- This gives us [tex]\(6x^2\)[/tex].
- Move on to the second term: [tex]\(\frac{-21x^2}{7x}\)[/tex].
- Divide the coefficients: [tex]\(\frac{-21}{7} = -3\)[/tex].
- Subtract the exponents of [tex]\(x\)[/tex]: [tex]\(x^{2-1} = x\)[/tex].
- This gives us [tex]\(-3x\)[/tex].
- Lastly, divide the third term: [tex]\(\frac{49x}{7x}\)[/tex].
- Divide the coefficients: [tex]\(\frac{49}{7} = 7\)[/tex].
- Subtract the exponents of [tex]\(x\)[/tex]: [tex]\(x^{1-1} = x^0\)[/tex], and [tex]\(x^0\)[/tex] is 1.
- This gives us [tex]\(+7\)[/tex].
2. Combine the Results:
- Combine the results from each term: [tex]\(6x^2 - 3x + 7\)[/tex].
Based on these calculations, the quotient is [tex]\(6x^2 - 3x + 7\)[/tex].
Therefore, the correct choice is:
[tex]\(6x^2 - 3x + 7\)[/tex]
