Interactive Coursebook (Online) of C10 Polynomials
C10 Polynomials
What’s on the Specification
| MM1.6 | Algebraic manipulation of polynomials, including:
|
| MM8.6 | Use algebraic techniques to determine where the graph of a function intersects the coordinate axes; appreciate the possible numbers of real roots that a general polynomial can possess. |
Learning Objectives
- Expand, collect, and factorise complex polynomial expressions.
- Perform algebraic division of polynomials by linear divisors (including those of the form $ax+b$ ) and quadratic divisors (including those of the form $a x^2+b x+c$ ).
- Understand and expertly apply the Factor Theorem to deduce linear and quadratic factors, and to identify the roots of higher-degree polynomials.
- Understand and apply the Remainder Theorem to evaluate the remainders of algebraic division and deduce unknown polynomial coefficients.
- Determine the exact intersections between polynomial graphs and the coordinate axes using purely algebraic techniques.
- Analyse the real roots of general polynomials, specifically appreciating the maximum possible number of real roots a polynomial of a given degree can possess.
Suggested Time
| Task | No. of Questions | Suggested Time |
|---|---|---|
| Examples | 18 | 180 min |
| Quiz | 8 | 20 min |
| Practice A | 35 | 75 min |
| Practice B | 20 | 75 min |
| Total | 81 | approx. 5-6 hrs |
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