- 1. Polynomials: Language, Value and Arithmetic
Recognise a polynomial and write it in standard form, state its degree, leading coefficient and constant term, find f(a) and f(x + h), find an unknown coefficient from a given value, and add, subtract and multiply polynomials.
- 2. Long Division by a Linear Divisor
Divide a polynomial by a linear divisor such as (x + 3), (x - 2) or (2x - 1) using long division, find the quotient and remainder, fill missing powers with zeros, write the division statement and check it.
- 3. Dividing by a Quadratic: the Division Identity
Divide a polynomial by a quadratic divisor, write the division identity P = DQ + R, use it to find unknown coefficients by equating coefficients, and find the other factor when a quadratic or repeated factor is given.
- 4. The Remainder Theorem
Find the remainder on dividing by (x - a), (ax - b) or a quadratic without dividing, using P(a); find unknown coefficients from remainder conditions and from equal remainders.
- 5. The Factor Theorem
Use the Factor Theorem to test whether a bracket is a factor, find unknown coefficients from a factor, choose the factor from a list, and use two factors or a quadratic factor to find two unknowns.
- 6. Factorising Fully and Finding Zeros
Factorise a polynomial completely using a given factor or a zero found by trial, tell the factors from the zeros of a polynomial, and handle grouping, repeated zeros and quartics.
- 7. Sketching Polynomial Graphs
Sketch a polynomial of degree 3 or less from its leading term, its zeros and its y-intercept, decide whether it crosses or touches the x-axis, and read an equation or the sign of y from a sketch.
- 8. Putting It All Together: Choosing the Tool
Read the wording of a polynomial question, choose the right tool from this unit, combine a factor and a remainder, compare two routes for a quadratic divisor, and answer whole WAEC and JAMB style questions.
