M5.1.3 For the adult
Dividing polynomials
Can I divide x³ + 2x² − 5x − 6 by x + 1 the way I divide 86 by 7?
What this chapter teaches
Polynomials are divided like numbers: divide the first terms, multiply back, subtract, bring down. The result is dividend = divisor × quotient + remainder, and the remainder has a lower degree than the divisor. The remainder theorem gives the remainder on dividing by x − a at once: it is f(a). The sign flips: dividing by x + 2 uses f(−2).
Three questions to ask
There is no one right wording. Listen for the idea.
- What number do you put into f when you divide by x + 5?
- Why does a missing power of x need a 0 in the long division?
- How can you check a long division by multiplying?
After the chapter, the learner can
- Divide x³ + 2x² − 5x − 6 by x + 1
- Find a remainder quickly with the remainder theorem
What they copy into their notebook
Divide first terms, multiply back, subtract, bring down. dividend = divisor × quotient + remainder. Remainder of f(x) ÷ (x − a) is f(a). Divisor x + 2 means a = −2.