Forming cubic polynomial from given zeros
If α, β, and γ are the zeros of a cubic polynomial, then the polynomial can be written as k(x-α)(x-β)(x-γ), where k is a non-zero constant.
Practice This ConceptMain explanation
Teacher explanation
To form a cubic polynomial, write one linear factor for each zero and multiply them. If the problem gives a leading coefficient, include it before expanding. This method is useful for direct construction questions and for checking whether given zeros are correct.
Example
If the zeros are 1, 2, and 3, a cubic polynomial is (x-1)(x-2)(x-3).
Simple analogy
Three zeros need three brackets.
Common confusion
Students sometimes forget one zero and write only a quadratic polynomial. A cubic needs three linear factors.
Exam tip
For three zeros, always write three factors before expanding. Do not skip any root.
Answer writing and exam use
1-mark use
Write the exact meaning of forming cubic polynomial from given zeros in one clean line.
2-mark use
Define forming cubic polynomial from given zeros and add one example or condition.
3-mark use
Explain forming cubic polynomial from given zeros, show the method or example, and mention the common mistake.
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