Zero Product Property

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 apply the Zero Product Property to solve (x - 5)(x + 6) = 0?

Back

Set each factor equal to zero: x - 5 = 0 or x + 6 = 0. This gives the solutions x = 5 and x = -6.

Front

What are the solutions (zeros) of the equation (2x + 5)(x - 6) = 0?

Back

The solutions are x = -5/2 and x = 6.

Front

In the equation (x + 2)(x - 3) = 0, what are the factors?

Back

The factors are (x + 2) and (x - 3).

Front

What is the relationship between solutions, roots, x-intercepts, and zeros of a polynomial?

Back

They are all the same; they refer to the values of x where the polynomial equals zero.

Front

What does it mean for a polynomial to have a zero at x = 3?

Back

It means that when x = 3 is substituted into the polynomial, the result is zero.

Front

How can you determine the number of solutions from the factors of a polynomial?

Back

The number of solutions corresponds to the number of distinct factors set to zero.

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms.

Front

If (x - 1)(x + 4) = 0, what are the solutions?

Back

The solutions are x = 1 and x = -4.

Front

What is the first step in solving a quadratic equation using the Zero Product Property?

Back

Factor the quadratic equation into two binomials.