Rational Zero Theorem

Front

What is the Rational Zero Theorem?

Back

The Rational Zero Theorem states that if a polynomial has rational roots, they can be expressed as the ratio of the factors of the constant term and the leading coefficient.

Front

List the possible rational zeros for the polynomial f(x) = 3x^5 - 5x^2 + x + 6.

Back

The possible rational zeros are ±1, ±2, ±3, ±6, ±1/3, ±2/3.

Front

How do you determine the possible rational zeros of a polynomial?

Back

To determine possible rational zeros, list all factors of the constant term and the leading coefficient, then form all possible ratios.

Front

What is the significance of the Rational Zero Theorem in polynomial equations?

Back

It helps in identifying potential rational solutions, which can simplify the process of finding actual roots.

Front

If a polynomial has a leading coefficient of 3 and a constant term of 6, what are the possible rational zeros?

Back

The possible rational zeros are ±1, ±2, ±3, ±6, ±1/3, ±2/3.

Front

What is the volume formula for a rectangular box?

Back

Volume = length × width × height.

Front

Given the dimensions of a box as length = x+1, width = x+3, height = x-3, how do you express the volume as a function of x?

Back

Volume V(x) = (x+1)(x+3)(x-3) = x^3 + x^2 - 9x - 9.

Front

If the volume of a box is 14 5/8, how do you find the value of x given the dimensions?

Back

Set the volume function equal to 14 5/8 and solve for x.

Front

What are the dimensions of a box if the height is 3 inches less than the width and the length is 2 inches more than twice the width?

Back

Let width = w, then height = w - 3 and length = 2w + 2.

Front

How do you set up an equation for the volume of a box?

Back

Volume = length × width × height, substitute the expressions for length, width, and height.