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Integrated Mathematics III
5. CC.HSA.APR.B.2
5.4 Polynomial synthetic division
Synthetic Division
A shortcut for dividing a polynomial by (x minus r) using only its coefficients.
What You'll Learn
Synthetic division divides a polynomial by (x minus r) using only coefficients.
Write the root r and the polynomial's coefficients (using 0 for missing terms).
Bring down, multiply by r, and add across the row to fill in the bottom row.
The bottom row gives the quotient's coefficients, one degree lower, plus the remainder.
Synthetic division only works for a linear divisor with leading coefficient 1.
What You'll Practice
1
Dividing polynomials by linear expressions using synthetic division
2
Adding placeholders for missing terms in polynomials
3
Adjusting quotients when divisors have coefficients other than 1
4
Writing division statements in both multiplication and quotient forms
Why This Matters
Synthetic division is a powerful time-saving technique you'll use throughout algebra and calculus. While long division always works, mastering synthetic division lets you solve polynomial division problems in a fraction of the time when dealing with linear divisors.
Before You Start — Make Sure You Can:
This Unit Includes
4 Video lessons
Practice exercises
Learning resources
Skills
Synthetic Division
Polynomials
Division Algorithm
Quotient and Remainder
Coefficients
Linear Divisors
OH Curriculum Aligned