Roots / Factors

Front

What are the zeros of a polynomial?

Back

The zeros of a polynomial are the values of x that make the polynomial equal to zero. They are also known as the roots of the polynomial.

Front

Solve the equation by factoring: x² - 6x + 8 = 0

Back

The solutions are x = 2 and x = 4.

Front

How many zeros does the parabola y = ax² + bx + c have?

Back

The number of zeros can be determined by the discriminant (b² - 4ac). If the discriminant is positive, there are 2 zeros; if it is zero, there is 1 zero; if negative, there are no zeros.

Front

What is the discriminant of a quadratic equation?

Back

The discriminant is the expression b² - 4ac in the quadratic formula, which determines the nature of the roots.

Front

How many solutions does the graph of a quadratic equation have if the discriminant is 0?

Back

If the discriminant is 0, the graph has exactly 1 solution (or 1 zero).

Front

What is a factor of a polynomial?

Back

A factor of a polynomial is a polynomial of lower degree that divides the polynomial without leaving a remainder.

Front

What is the relationship between the degree of a polynomial and the number of zeros?

Back

The degree of a polynomial indicates the maximum number of zeros it can have.

Front

Solve the equation by factoring: x² - 5x + 6 = 0

Back

The solutions are x = 2 and x = 3.

Front

What does it mean for a polynomial to be factored completely?

Back

A polynomial is factored completely when it is expressed as a product of its irreducible factors.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.