Solving Polynomial Equations in Factored Form

Front

What is a polynomial equation in factored form?

Back

A polynomial equation expressed as a product of its factors, typically set to zero, e.g., (x - a)(x - b) = 0.

Front

How do you solve a polynomial equation in factored form?

Back

Set each factor equal to zero and solve for the variable. For example, from (x - 3)(x + 6) = 0, set x - 3 = 0 and x + 6 = 0.

Front

What are the roots of the equation (x - 3)(x + 6) = 0?

Back

The roots are x = 3 and x = -6.

Front

What is the significance of the roots of a polynomial equation?

Back

The roots are the values of x that make the equation true (where the graph intersects the x-axis).

Front

Solve for x: (2x - 1)(x + 4) = 0

Back

x = 1/2 and x = -4.

Front

What does it mean if a polynomial equation has multiple roots?

Back

It means that the same root appears more than once, indicating that the graph touches the x-axis at that point.

Front

Solve for x: (x + 2)(x - 3) = 0

Back

x = -2 and x = 3.

Front

What is the zero product property?

Back

If the product of two or more factors is zero, at least one of the factors must be zero.

Front

Solve for x: (2x - 8)(x + 5) = 0

Back

x = 4 and x = -5.

Front

What is the first step in solving (2x + 5)(5x - 2) = 0?

Back

Set each factor equal to zero: 2x + 5 = 0 and 5x - 2 = 0.