Unit 2, Lesson 13
Polynomial Division (Part 2)
Algebra 2
13.1
Warm-up
What do you notice? What do you wonder?
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What do you notice? What do you wonder?
In earlier grades, we learned that one way to divide numbers, like 1,573 divided by 11, is by using long division.
Long division of 1,573 divided by 11.
4 rows.
Top row: 1.
Second row: 11 on the left, long division symbol with 1,573 inside.
Third row: 11.
Horizontal line.
Fourth row: 4.
Long division of 1,573 divided by 11.
6 rows.
Top row: 14.
Second row: 11 on the left, long division symbol with 1,573 inside.
Third row: 11.
Horizontal line.
Fourth row: 47.
Fifth row: 44.
Horizontal line.
Sixth row: 3.
Long division of 1,573 divided by 11.
8 rows.
Top row: 143.
Second row: 11 on the left, long division symbol with 1,573 inside.
Third row: 11.
Horizontal line.
Fourth row: 47.
Fifth row: 44.
Horizontal line.
Sixth row: 33.
Seventh row: 33.
Horizontal line.
Eighth row: 0.
Here the division has been completed in stages, focusing on the highest power of 10 (1,000) in the dividend 1,573, and working down. This long division shows that .
Similar to integers, we can also use long division on polynomials. Instead of focusing on powers of 10, in polynomial long division we focus on powers of . Just as we started with the highest power or 10, we start with the highest power of , the leading term, and work down to the constant term. For example, here is divided by completed in three stages. Notice how terms of the same degree are in the same columns.
At each stage, the focus is only on the term with the largest exponent that’s left. At the conclusion, we can see that .