Question 1

What is a polynomial?

Accepted Answer

A polynomial is an algebraic expression made of terms of the form aₙxⁿ, where n is a non-negative integer. For example, 3x² − 5x + 2 and x⁵ − 1 are polynomials; 1/x and √x are not.

Question 2

What is the degree of a polynomial?

Accepted Answer

The degree is the highest power of the variable that appears with a nonzero coefficient. For example, −x³ + 2x² − 1 has degree 3, and x⁵ − 1 has degree 5.

Question 3

How do I factor a polynomial?

Accepted Answer

Common methods: pull out the greatest common factor; use special identities like x² − y² = (x + y)(x − y) or x³ ± y³; factor by grouping; factor a quadratic trinomial using the ac-method; for higher degrees, apply the Rational Root Theorem followed by synthetic division.

Question 4

What is the difference between polynomial long division and synthetic division?

Accepted Answer

Long division works for any divisor polynomial. Synthetic division is a shortcut that only works when the divisor is linear (of the form x − k). For higher-degree divisors, use long division.

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