A polynomial is an expression of one or more variables, with coefficients and exponents. It can have addition, subtraction, and multiplication operations. Let's take an example to understand this concept better.

Consider the polynomial expression: 3x^2 + 4x - 6. Here, '3', '4', and '-6' are the coefficients, 'x' is the variable, and '2' is the exponent. The terms of this expression are '3x^2', '4x', and '-6'.

Factoring a polynomial means expressing it as a product of its factors. It helps us simplify and solve equations more easily.

Let's say we have the polynomial expression: 2x^2 + 7x + 3. We can factor this by looking for two binomials whose product equals the original expression. In this case, the factored form of the polynomial would be (2x + 1)(x + 3). By multiplying these binomials, we can verify that it gives us the original expression.

Factoring can also help us find the solutions to quadratic equations by setting the factored polynomial equal to zero. Solving for x will give us the values of x at which the polynomial equals zero, also known as the roots or zeros of the equation.