Answer:
D) A = 2p and B = 1/p
Step-by-step explanation:
To divide this,
we first see how many times 3p will go into 6p².
[tex]\frac{6p^2}{3p} = 2p[/tex]
It will go in 2p times; this goes up top of the problem.
Multiplying back through, we have
[tex]2p*3p = 6p^2[/tex]
Subtracting this from the first term under the box, we have
[tex]6p^2-6p^2= 0.[/tex]
This cancels. Bring down the next term, 9p.
See how many times 3p goes into 9p = [tex]\frac{9p}{3p}=3[/tex]
it goes in 3 times. This goes up top, beside the 2p. We separate them with a +, since the 3 is positive.
Multiplying back through, we have 3(3p) = 9p.
Subtract this from the line above; 9p-9p = 0.
Bring down the last term, 3.
Since this is not 0, this is the remainder.
This gives us
2p + 3 R 3;
writing this as a rational expression, we have
[tex]2p + 3 + \frac{3}{3p}[/tex]
The remainder term, [tex]\frac{3}{3p}[/tex], will simplify to 1/1p or 1/p;
this gives us
[tex]2p + 3 + \frac{1}{p}[/tex]
Therefore, the answer is A = 2p and B = 1/p
