Front

What are the zeros of a function?

Back

The zeros of a function are the values of x for which the function equals zero. They are the x-intercepts of the graph of the function.

Front

How do you represent exponential decay in an equation?

Back

Exponential decay can be represented by the equation y = a(1 - r)^x, where a is the initial amount, r is the decay rate, and x is time.

Front

What does it mean if p(5) = -8 for a polynomial p(x)?

Back

If p(5) = -8, it means that when x = 5 is substituted into the polynomial, the output is -8. This indicates that (x-5) is not a factor of p(x), and the remainder when p(x) is divided by (x-5) is -8.

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that the remainder of the division of a polynomial p(x) by (x - c) is equal to p(c).

Front

How do you find the value of x that satisfies an equation?

Back

To find the value of x that satisfies an equation, isolate x on one side of the equation using algebraic operations.

Front

What is the significance of evaluating p(-2) when dividing by (x + 2)?

Back

Evaluating p(-2) gives the remainder when the polynomial p(x) is divided by (x + 2).

Front

What is a polynomial function?

Back

A polynomial function is a function that can be expressed in the form p(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0, where a_n, a_{n-1}, ..., a_0 are constants and n is a non-negative integer.

Front

What is the general form of an exponential decay function?

Back

The general form of an exponential decay function is y = a(1 - r)^x, where a is the initial value and r is the decay rate.

Front

What does it mean for a number to be a zero of a polynomial?

Back

A number is a zero of a polynomial if substituting that number into the polynomial results in a value of zero.

Front

How do you determine the factors of a polynomial?

Back

To determine the factors of a polynomial, you can use methods such as synthetic division, factoring, or the Rational Root Theorem.