NSW Y11 Maths - Extension 1 Polynomials Factor Theorem

Resources for Factor Theorem

• Questions

  27

  With Worked Solution
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• Video Tutorials

  2

  
  
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• HSC Questions

  5

  With Worked Solution
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Factor Theorem Theory

NSW Syllabus Reference

NSW Syllabus Reference: ME-F2.1: Remainder and factor theorems. This will require student to 

• define a general polynomial in one variable, $x$, of degree $n$ with real coefficients to be the expression: $a_n{x}^n+a_{n-1}{x}^{n-1}+\cdots +a_2{x}^2+a_{1}x+a_0$, where $a_n\ne 0$
• use division of polynomials to express $P(x)$ in the form $P(x)=A(x).Q(x)+R(x)$ where $\mathrm{deg}R(x)<\mathrm{deg}A(x)$ and $A(x)$ is a linear or quadratic divisor, $Q(x)$ the quotient and $R(x)$ the remainder
• prove and apply the factor theorem and the remainder theorem for polynomials and hence solve simple polynomial equations (ACMSM089, ACMSM091)

Ref: https://educationstandards.nsw.edu.au/