Mathematics (AS)·Algebra · NSSCAS 2.1.4
The remainder & factor theorems
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In this lesson you'll learn two of the most useful shortcuts in AS algebra. You'll find the remainder of a polynomial division in one line using the remainder theorem, and decide whether a bracket is a factor using the factor theorem. You'll then master the big exam skill of fully factorising a cubic and solving it, and you'll find unknown coefficients from a given factor or remainder. Every step is worked slowly on the board.
What you'll learn in this lesson
By the end you should be able to (NSSCAS Mathematics (AS) 2.1.4):
- Apply the remainder theorem to find the remainder when a polynomial is divided by a linear divisor.
- Apply the factor theorem to test and confirm factors of a polynomial.
- Use the factor theorem to fully factorise a cubic and solve a polynomial equation for all its roots.
- Use the factor and remainder theorems to evaluate unknown coefficients, including two-condition simultaneous problems.
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