Flashcard #12 - Algebra 2

Front

What is the inverse of the coordinates (1, 2) (3, 8) (-3, 6)?

Back

(2, 1) (8, 3) (6, -3)

Front

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

Back

1/3, 2/3, 1, 2, 3, 6, -1/3, -2/3, -1, -2, -3, -6

Front

Find all the real zeros of the function f(x) = 2x^3 - 19x^2 + 38x + 24 given that (x-4) is a factor.

Back

x = 4, -1/2, 6

Front

What is the inverse of the function f(x) = 2x + 3?

Back

f^(-1)(x) = (x - 3)/2

Front

Perform the operation: (x^2 + 2x) + (3x^2 - x).

Back

4x^2 + x

Front

Define a rational zero.

Back

A rational zero is a solution to a polynomial equation that can be expressed as a fraction p/q, where p and q are integers.

Front

What is the Remainder Theorem?

Back

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

Front

Explain the Factor Theorem.

Back

The Factor Theorem states that (x - c) is a factor of the polynomial f(x) if and only if f(c) = 0.

Front

What is the definition of a polynomial function?

Back

A polynomial function is a function that can be expressed in the form f(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

How do you find the zeros of a polynomial function?

Back

To find the zeros of a polynomial function, set the function equal to zero and solve for x.