College Algebra & Trigonometry, 2018a

2.6. POLYNOMIAL LONG DIVISION 115
2.6 Polynomial Long Division
Polynomial long division has many similarities to numerical long division, so it
is important that we understand how and why numerical long division works
the way it does before discussing polynomial long division. First the HOW?
Given the numerical problem 87, 462÷38, the first step is to determine the highest
place value in the answer.
2
38)87, 462
Often the first step in numerical long division is to say “Does 38 divide into 8?”
“No.” “Does 38 divide into 87?” “Yes.” This tells us that the first digit in the
answer will be over the 7 in 87,462, and consequently will be in the thousands
place. Once we know that the first digit in the answer will be in the thousands
place, the next question is “How many thousands?” We can determine that 2 ∗
38=76but 3∗38 = 114 (too big), so we know that the first digit in the answer will
be 2. Then we subtract, include the 4 and examine what is left over to continue.
2
38)87, 462
−76
114
Here, we see that 114 ÷ 38 = 3, so we know that the next digit in the answer will
be 3.
23
38)87, 462
−76
114
−114
0006
After including the 6, we can see that 38 does not divide evenly into 6, so we put
a zero as the next digit in our answer and proceed: