Answer :
To divide [tex]\(\frac{27x^4 + 21x^3 + 23x^2}{3x^2}\)[/tex] and simplify the expression, follow these steps:
1. Divide each term separately by [tex]\(3x^2\)[/tex]:
- First term:
[tex]\[
\frac{27x^4}{3x^2} = \frac{27}{3} \cdot \frac{x^4}{x^2} = 9x^{4-2} = 9x^2
\][/tex]
- Second term:
[tex]\[
\frac{21x^3}{3x^2} = \frac{21}{3} \cdot \frac{x^3}{x^2} = 7x^{3-2} = 7x
\][/tex]
- Third term:
[tex]\[
\frac{23x^2}{3x^2} = \frac{23}{3} \cdot \frac{x^2}{x^2} = \frac{23}{3} \cdot x^{2-2} = \frac{23}{3} \cdot x^0 = \frac{23}{3} \cdot 1 = \frac{23}{3}
\][/tex]
2. Combine the simplified terms:
The expression simplifies to:
[tex]\[
9x^2 + 7x + \frac{23}{3}
\][/tex]
This is the simplified expression after dividing by [tex]\(3x^2\)[/tex].
1. Divide each term separately by [tex]\(3x^2\)[/tex]:
- First term:
[tex]\[
\frac{27x^4}{3x^2} = \frac{27}{3} \cdot \frac{x^4}{x^2} = 9x^{4-2} = 9x^2
\][/tex]
- Second term:
[tex]\[
\frac{21x^3}{3x^2} = \frac{21}{3} \cdot \frac{x^3}{x^2} = 7x^{3-2} = 7x
\][/tex]
- Third term:
[tex]\[
\frac{23x^2}{3x^2} = \frac{23}{3} \cdot \frac{x^2}{x^2} = \frac{23}{3} \cdot x^{2-2} = \frac{23}{3} \cdot x^0 = \frac{23}{3} \cdot 1 = \frac{23}{3}
\][/tex]
2. Combine the simplified terms:
The expression simplifies to:
[tex]\[
9x^2 + 7x + \frac{23}{3}
\][/tex]
This is the simplified expression after dividing by [tex]\(3x^2\)[/tex].
