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Section 5.7, dividing with a remainder.
Like the last clip, let's take a look at first, what kind of
result we get with doing it with arithmetics when we have
a remainder problem, and then we'll look at how
we do it for algebra.
The process is exactly the same, divide, multiply,
subtract, bring down.
So divide first number.
First number, 6 by 2 is 3.
Multiply, 3 times 2 is 6, which we subtract.
6 minus 6 goes away.
Bring down, 5.
Start over again.
Divide, 5 by 2.
Well, 2 fits in twice is the most.
Multiply, 2 times 2 is 4.
Subtract, we're going to subtract that answer.
It doesn't cross out, it gives us a 1, and bring
down the next guy.
Start over again, 19 by 2.
Well, that goes in 9 times is the most.
Multiply, 9 times 2, 18.
We're going to subtract that number, that gives us a 1.
And there's nothing left to bring down,
so that 1 is a remainder.
The way we would write that final answer is 329 remainder
of 1 divided by the divisor of 2.
So let's take a look at how we'll do it with algebra, and
we're going to do the same thing with the remainder when
we have algebra.
We're going to take the remainder and make a fraction
part out of it.
The remainder will be the numerator, the divisor, on the
outside, is going to be the denominator.
So let's take the problem p squared plus 2p plus 20 all
being divided by p plus 6.
You will divide, multiply, subtract, bring down.
First term by first term, p squared over p, that leaves us
with a p, the answer goes up top.
We take that answer and we multiply it and distribute
through the p plus 6.
p times p plus 6 gives us p squared plus 6p.
We're going to take that result and
subtract it over here.
And remember, put parentheses around it when you subtract
it, so you remember to distribute your minus sign.
p squared minus p squared is gone, 2p take away 6p will be
minus 4p, bring down, plus 20.
Now, we're starting over again.
Divide, multiply, subtract, bring down.
Minus 4p divided by p, first term by first term again.
First term by first term, minus 4p over p, leaves us
with minus 4.
So we take that minus 4, put it on top, and then we take
the minus 4 and multiply it times p plus 6.
So minus 4 times p plus 6 is minus 4p takeaway 24.
We're going to take that result and
subtract it right here.
These two cancel out.
20 minus a minus is add the opposite, so it's plus 24,
leaves us with a 4.
There's nothing left to bring down, so we're not going to
continue repeating the process.
We're going to have a remainder of 4.
To write the final answer--
and I'm going to move the final answer down below here
so we could look at it if it better.
We don't want to leave it with an R4, we want to express this
remainder just like we do with arithmetics, is the remainder
is the numerator and the denominator is the
divisor, p plus 6.
So our final answer is p takeaway 4, and this is a
positive 4, so we're going to say, plus 4 over p plus 6.
And that would be the final answer.