Answer :
To solve the problem of finding the quotient when the expression [tex]\(9x^4 + 19x^2 + 8x^2 + 12\)[/tex] is divided by 3, follow these steps:
1. Combine Like Terms:
- The original expression is [tex]\(9x^4 + 19x^2 + 8x^2 + 12\)[/tex].
- Notice that the like terms [tex]\(19x^2\)[/tex] and [tex]\(8x^2\)[/tex] can be combined.
- Combine them: [tex]\(19x^2 + 8x^2 = 27x^2\)[/tex].
- The simplified expression is [tex]\(9x^4 + 27x^2 + 12\)[/tex].
2. Divide the Entire Expression by 3:
- To find the quotient, divide each term in the expression [tex]\(9x^4 + 27x^2 + 12\)[/tex] by 3.
- Divide the first term: [tex]\(\frac{9x^4}{3} = 3x^4\)[/tex].
- Divide the second term: [tex]\(\frac{27x^2}{3} = 9x^2\)[/tex].
- Divide the third term: [tex]\(\frac{12}{3} = 4\)[/tex].
3. Write the Quotient:
- The result of dividing the entire expression by 3 is [tex]\(3x^4 + 9x^2 + 4\)[/tex].
Therefore, the quotient when [tex]\(9x^4 + 19x^2 + 8x^2 + 12\)[/tex] is divided by 3 is [tex]\(3x^4 + 9x^2 + 4\)[/tex].
1. Combine Like Terms:
- The original expression is [tex]\(9x^4 + 19x^2 + 8x^2 + 12\)[/tex].
- Notice that the like terms [tex]\(19x^2\)[/tex] and [tex]\(8x^2\)[/tex] can be combined.
- Combine them: [tex]\(19x^2 + 8x^2 = 27x^2\)[/tex].
- The simplified expression is [tex]\(9x^4 + 27x^2 + 12\)[/tex].
2. Divide the Entire Expression by 3:
- To find the quotient, divide each term in the expression [tex]\(9x^4 + 27x^2 + 12\)[/tex] by 3.
- Divide the first term: [tex]\(\frac{9x^4}{3} = 3x^4\)[/tex].
- Divide the second term: [tex]\(\frac{27x^2}{3} = 9x^2\)[/tex].
- Divide the third term: [tex]\(\frac{12}{3} = 4\)[/tex].
3. Write the Quotient:
- The result of dividing the entire expression by 3 is [tex]\(3x^4 + 9x^2 + 4\)[/tex].
Therefore, the quotient when [tex]\(9x^4 + 19x^2 + 8x^2 + 12\)[/tex] is divided by 3 is [tex]\(3x^4 + 9x^2 + 4\)[/tex].
