Maths Extension 1 Year 11 - Module 2 - Lesson 1
Introduction to Polynomials
Name
Date
Class
1. Lesson focus
Polynomial structure and evaluation. A polynomial has non-negative integer powers of x; its degree is the greatest exponent with a non-zero coefficient.
Success criteria
- Apply the lesson method accurately in a routine example.
- Show each algebraic or domain step and check the result.
- Explain why the method and restrictions fit the question.
2. Worked practice
2. Evaluate p(x)=x³−2x²+x+4 at x=−2.
3. Write the leading term of −3x⁵+2x²−1 and state its end behaviour.
3. Challenge
Is 5x²+1/x−3 a polynomial? Explain.
4. Multiple choice
Which expression is a polynomial in x?
A. 3x⁴−2x+1
B. x²+1/x
C. √x+3
D. 4ˣ+1
Worked answer key
Compare each step with your working. Keep stated intervals, domains and restrictions in your final answer.
1. State the degree and leading coefficient of 4x³−2x+7.
Degree 3; leading coefficient 4.
2. Evaluate p(x)=x³−2x²+x+4 at x=−2.
p(−2)=−8−8−2+4=−14.
3. Write the leading term of −3x⁵+2x²−1 and state its end behaviour.
Leading term −3x⁵; odd degree with negative leading coefficient, so left end rises and right end falls.
Challenge. Is 5x²+1/x−3 a polynomial? Explain.
No: x⁻¹ is a negative power, which is not allowed in a polynomial.
Multiple choice. Which expression is a polynomial in x?
Correct answer: A. Only non-negative integer powers of x are allowed; the other choices contain a negative, fractional or variable exponent.
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