Factor Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What does it mean to factor a polynomial?

Back

Factoring a polynomial means expressing it as a product of its factors, which are polynomials of lower degrees.

Front

What is the difference between prime and composite polynomials?

Back

A prime polynomial cannot be factored into the product of two non-constant polynomials, while a composite polynomial can.

Front

Factor the polynomial: x² - 16

Back

(x - 4)(x + 4)

Front

Factor the polynomial: n² + 16n + 63

Back

(n + 7)(n + 9)

Front

Factor the polynomial: 2x² - 13x + 15

Back

(2x - 3)(x - 5)

Front

Factor the polynomial: 3a² + 4a + 1

Back

(3a + 1)(a + 1)

Front

Factor the polynomial: x² - 49

Back

(x + 7)(x - 7)

Front

What is the zero-product property?

Back

The zero-product property states that if the product of two factors is zero, then at least one of the factors must be zero.

Front

How do you check if a polynomial is factorable?

Back

To check if a polynomial is factorable, look for common factors, apply the quadratic formula, or use methods like grouping or synthetic division.