Question

Consider the division of 4h2 + 2h + 6 by 2h.







What are the values of A and B?

A = 2 and B = 1
A = 2h and B = 1
A = and B =
A = and B =

Answer 1

To divide the polynomial \( 4h^2 + 2h + 6 \) by \( 2h \), we can perform polynomial long division or simply use the property of division.

1. Start with the first term: divide \( 4h^2 \) by \( 2h \):
\[
\frac{4h^2}{2h} = 2h
\]
This will give us the first part of the quotient, which is \( A = 2h \).

2. Now, multiply \( 2h \) by \( 2h \) and subtract it from \( 4h^2 + 2h + 6 \):
\[
4h^2 + 2h + 6 - (2h \cdot 2h) = 4h^2 + 2h + 6 - 4h^2 = 2h + 6
\]

3. Next, divide \( 2h \) by \( 2h \):
\[
\frac{2h}{2h} = 1
\]
This gives us the second part of the quotient, which is \( B = 1 \).

4. Finally, combine the results of the division:
\[
\frac{4h^2 + 2h + 6}{2h} = 2h + 1 + \frac{6}{2h}
\]

Therefore, \( A = 2h \) and \( B = 1 \).

So the values are:
- \( A = 2h \)
- \( B = 1 \)