Cubic polynomial and its zeros
A cubic polynomial is a polynomial of degree 3, usually written as ax^3+bx^2+cx+d where a is not zero. Its zeros are the values of x that make the polynomial equal to 0.
Practice This ConceptMain explanation
Teacher explanation
A cubic polynomial can have up to three zeros. In many exam questions, students need to identify the zeros by factorising, by using a given factor, or by checking a graph. The important idea is that each zero makes the polynomial vanish at that x-value.
Example
For x^3-6x^2+11x-6, the zeros are 1, 2, and 3.
Simple analogy
Cubic can give three x-axis hits.
Common confusion
Students sometimes stop after finding two zeros and forget that a cubic polynomial may have three zeros.
Exam tip
After factorising a cubic polynomial, keep solving until the expression is fully broken into linear factors.
Answer writing and exam use
1-mark use
Write the exact meaning of cubic polynomial and its zeros in one clean line.
2-mark use
Define cubic polynomial and its zeros and add one example or condition.
3-mark use
Explain cubic polynomial and its zeros, show the method or example, and mention the common mistake.
Practice this concept with focused MCQs
Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.
Help improve this page
Found something confusing, incorrect, or missing?