Solving Polynomials by Factoring

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 zero-product property?

Back

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

Front

Solve: x² - 16 = 0

Back

x = ±4

Front

What is the difference of squares formula?

Back

The difference of squares formula states that a² - b² = (a - b)(a + b).

Front

Solve: x² - 25 = 0

Back

x = ±5

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0.

Front

Solve: x² + 6x + 9 = 0

Back

x = -3 (a perfect square trinomial).

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial, such as (a + b)² = a² + 2ab + b².

Front

Solve: x² + 4x + 4 = 0

Back

x = -2 (a perfect square trinomial).