Polynomials Extension 1

 HSC polynomials Extension 1 builds algebraic fluency that underpins much of the Extension 1 and 2 courses. You need confident factorisation, remainder and factor theorem applications, and the ability to sketch polynomial graphs from their roots.

Core Extension 1 polynomial skills

• Factorisation — common factors, grouping, sum and difference of cubes
• Remainder theorem and factor theorem
• Division of polynomials — long division and equating coefficients
• Graph sketching — turning points, inflection, multiplicity of roots
• Solving polynomial equations and inequalities

Dedicated Extension 1 booklet

HSC Polynomials Extension 1 on Vu's Maths Hub covers factorisation, remainder theorem, and polynomial graphs with worked examples.

Extension 2 polynomials

When you move to Extension 2, the algebra gets harder — complex roots, conjugate pairs, and relationships between coefficients and roots. See HSC Polynomials and HSC Complex Numbers.

Also useful: HSC Functions for transformations and HSC Induction for polynomial identities proved by induction.

NESA-aligned, free HSC Maths booklets — your tutoring alternative for NSW Year 12.