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Polynomials Practice
Solve chapter-level practice questions for Polynomials with reveal-only solutions and quick revision support.
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Practice Set 1 — Degree, Zeroes, Remainder Theorem
Identifying polynomials, evaluating, and using the Remainder Theorem.
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Practice Set 2 — Factorisation and Identities
Splitting the middle term, the Factor Theorem for cubics, and identities.
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Quick Q&A Before You Revise
Is $\sqrt{2}x + 3$ a polynomial?
Yes. The coefficient can be any real number, including an irrational number like √2. What matters is that the power of the variable (here 1) is a whole number.
What is the difference between a zero of a polynomial and the value of a polynomial?
The value of p(x) at x = a is simply p(a). A zero is a special value of x for which p(a) = 0.
How does the Factor Theorem help in factorising a cubic polynomial?
Try small integer values (factors of the constant term). If p(a) = 0, then (x − a) is a factor. Divide the cubic by (x − a) to get a quadratic, which can then be factorised by splitting the middle term.
How many zeroes can a polynomial of degree n have?
At most n real zeroes. A linear polynomial has exactly one; a quadratic has at most two; a cubic has at most three.
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