Unit 2, Lesson 13
Polynomial Division (Part 2)
Integrated Math 3
13.1
Warm-up
Notice and Wonder: Different Divisions
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
At each stage, the focus is only on the term with the largest exponent that’s left. At the conclusion, we can see that