Polynomial Linear Factors and Zeros

Front

What are the zeros of a polynomial function?

Back

The zeros of a polynomial function are the values of x for which the function equals zero. They represent the x-coordinates where the graph of the function intersects the x-axis.

Front

What is a linear factor of a polynomial?

Back

A linear factor of a polynomial is an expression of the form (x - c), where c is a constant. The linear factors of a polynomial can be multiplied together to form the polynomial.

Front

How do you find the zeros of a polynomial?

Back

To find the zeros of a polynomial, set the polynomial equal to zero and solve for x. This can involve factoring, using the quadratic formula, or graphing.

Front

What does it mean to factor a polynomial?

Back

Factoring a polynomial means expressing it as a product of its linear factors. For example, x^2 - 16 can be factored into (x - 4)(x + 4).

Front

What is the relationship between zeros and factors?

Back

Each zero of a polynomial corresponds to a linear factor of the polynomial. If x = c is a zero, then (x - c) is a factor.

Front

What is the significance of the x-axis in relation to polynomial functions?

Back

The x-axis represents the values of x for which the function equals zero. The points where the graph crosses the x-axis are the zeros of the function.

Front

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

Back

The zeros are x = 3 and x = -2.

Front

What does it mean to 'find the zeros' of a function graphically?

Back

Finding the zeros graphically means identifying the points where the graph intersects the x-axis.

Front

What is the factored form of x^2 - 9?

Back

The factored form is (x - 3)(x + 3).

Front

How can you verify the zeros of a polynomial?

Back

You can verify the zeros by substituting them back into the polynomial equation to see if the result is zero.