Solving Polynomials by Factoring

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists 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: x^2 - 16 = 0

Back

x = ±4

Front

What is the difference of squares formula?

Back

The difference of squares formula states that a^2 - b^2 = (a - b)(a + b).

Front

Solve: x^2 - 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 ax^2 + bx + c = 0.

Front

How do you factor x^2 + 5x + 6?

Back

x^2 + 5x + 6 = (x + 2)(x + 3).

Front

What is the sum and product of the roots in a quadratic equation?

Back

For a quadratic equation ax^2 + bx + c = 0, the sum of the roots is -b/a and the product of the roots is c/a.

Front

Solve: x^2 + 7x + 10 = 0

Back

x = -2, -5