Answer:
[tex]3x+3+\frac{1}{x+2}[/tex]
Step-by-step explanation:
We are to divide the polynomial [tex]3x^2 + 9x + 7[/tex] by [tex]x+2[/tex].
For that, we will first divide the leading coefficient of the numerator [tex]\frac{3x^2}{x}[/tex] by the divisor.
So we get the quotient: [tex]3x[/tex] and will multiply the divisor [tex]x+2[/tex] by [tex]3x[/tex] to get [tex]3x^2+6x[/tex].
Next, we will subtract [tex]3x^2+6x[/tex] from [tex]3x^2 + 9x + 7[/tex] to get the remainder [tex]3x+7[/tex].
Therefore, we get [tex]3x+\frac{3x+7}{x+2}[/tex].
Now again, dividing the leading coefficient of the numerator by the divisor [tex]\frac{3x}{x}[/tex] to get quotient [tex]3[/tex].
Then we will multiply [tex]x+2[/tex] by [tex]3[/tex] to get [tex]3x+6[/tex].
Then, we will subtract [tex]3x+6[/tex] from [tex]3x+7[/tex] to get the new remainder [tex]1[/tex].
Therefore, [tex]\frac{3x^2 + 9x + 7}{x+2}=3x+3+\frac{1}{x+2}[/tex]
