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Any polynomial p(x) of degree n ≥ 1 may be expressed as?

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Any polynomial p(x) of degree n ≥ 1 may be expressed as? Answer: p(x) = (x - r)q(x) + k

This is due to the Factor Theorem, which states that if p(r) = 0, then (x - r) is a factor of p(x). Since a polynomial of degree n ≥ 1 has n roots, it can be factored into n linear factors (x - r1)(x - r2)...(x - rn). Combining these factors, we get the desired form p(x) = (x - r)q(x)k, where q(x) is a polynomial of degree n-1.

Question context

This question is part of 📏 Arithmetic Aptitude within the broader 🧠 Aptitude Mastery subject and appears in the SPSC – Sindh Public Service Commission preparation collection. Reviewing the answer together with nearby questions helps reinforce the underlying concept and identify how it may appear in competitive exams.