Math 3 EOC - Numbers/Quantity/Algebra

Front

What is a factor in polynomial expressions?

Back

A factor is a polynomial that divides another polynomial without leaving a remainder.

Front

What does it mean for a zero of a function to have multiplicity?

Back

Multiplicity refers to the number of times a particular zero is repeated in the function's factorization.

Front

How do you determine the zeros of a polynomial function?

Back

To find the zeros, set the polynomial equal to zero and solve for the variable.

Front

What is the significance of the degree of a polynomial?

Back

The degree of a polynomial indicates the highest power of the variable and determines the maximum number of zeros.

Front

What is the relationship between the roots and factors of a polynomial?

Back

Each root of a polynomial corresponds to a factor of the form (x - root).

Front

How can you verify if (x - a) is a factor of a polynomial?

Back

Use synthetic division or the Remainder Theorem; if the remainder is zero, (x - a) is a factor.

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that the remainder of the division of a polynomial f(x) by (x - a) is f(a).

Front

What are real zeros of a function?

Back

Real zeros are the values of x for which the function f(x) = 0.

Front

How do you find the real zeros of a cubic polynomial?

Back

Factor the polynomial or use the Rational Root Theorem to identify possible rational zeros.

Front

What is the difference between a root and a zero?

Back

A root is a solution to the equation f(x) = 0, while a zero is the x-value where the function intersects the x-axis.