1st Semester Review (Part 1)- Algebra 3

Front

What is direct variation?

Back

Direct variation is a relationship between two variables where one variable is a constant multiple of the other. It can be expressed as y = kx, where k is a non-zero constant.

Front

If y = 39 when x = 3, what is the value of y when x = 2 in a direct variation?

Back

y = 26 when x = 2.

Front

What are rational zeros in a polynomial function?

Back

Rational zeros are the possible values of x that make the polynomial equal to zero, expressed as fractions or integers.

Front

How do you find all possible rational zeros of a polynomial?

Back

Use the Rational Root Theorem, which states that any rational solution, expressed as p/q, has p as a factor of the constant term and q as a factor of the leading coefficient.

Front

What is the Rational Root Theorem?

Back

The Rational Root Theorem provides a way to find all possible rational roots of a polynomial equation by considering the factors of the constant term and the leading coefficient.

Front

What is a polynomial function?

Back

A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.

Front

What is the significance of zeros in a polynomial function?

Back

Zeros of a polynomial function are the values of x for which the function equals zero, indicating the x-intercepts of the graph.

Front

How do you write a polynomial function with given zeros?

Back

To write a polynomial function with given zeros, use the factored form: P(x) = a(x - r1)(x - r2)...(x - rn), where r1, r2, ..., rn are the zeros.

Front

What does it mean for (x - 2) to be a factor of a polynomial?

Back

If (x - 2) is a factor of a polynomial, it means that when the polynomial is divided by (x - 2), the remainder is zero.

Front

How can you determine if (x - 2) is a factor of f(x) = x^3 - 8x^2 + 14x - 4?

Back

Use synthetic division or polynomial long division to check if the remainder is zero when dividing f(x) by (x - 2).