Algebra — Expressions
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Polynomial Expressions

✏️ Algebra — Expressions
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Polynomial Expressions

Read and interpret the structure of polynomial expressions.

A polynomial is an expression consisting of variables and coefficients combined using addition, subtraction, and non-negative integer exponents. Understanding the parts of a polynomial — terms, coefficients, degree, and leading term — is essential for all of algebra.

Anatomy of a Polynomial

3x² − 7x + 4Terms: 3x², −7x, 4Coefficients: 3, −7, 4 (constant term)Degree: 2 (highest exponent)Leading term: 3x²

The degree determines the polynomial's name: degree 1 = linear, degree 2 = quadratic, degree 3 = cubic.

P(x)=anxn+an−1xn−1+⋯+a1x+a0P(x) = a_n x^n + a_{n-1} x^{n-1} + \cdots + a_1 x + a_0

Factoring reveals the structure hidden inside a polynomial. A factored form like (x − 2)(x + 5) immediately shows the roots (x = 2 and x = −5), while the expanded form 2x² + 6x − 4 = 2(x² + 3x − 2) reveals a common factor of 2.

🧩Factoring Out the GCF
Factor 6x³ + 9x² − 3x. The GCF is 3x. Dividing each term: 6x³/3x = 2x², 9x²/3x = 3x, −3x/3x = −1. Result: 3x(2x² + 3x − 1).
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Remember This!

Always check for a greatest common factor (GCF) before applying any other factoring technique. Pulling out the GCF first simplifies everything that follows.

✏️ Try It!

What is the degree of the polynomial 5x⁴ − 3x² + 7x − 2?

Take Quiz 📝 — 24 Questions