Math 3 wk 3

Front

What are the zeros of the polynomial f(x) = 2x^3 + 5x^2 - 6x - 9?

Back

The zeros are -1, -3, and 3/2.

Front

Expand the expression (x - 4)(x - 6).

Back

The expanded form is x^2 - 10x + 24.

Front

What is the standard form of the function y = (x + 1)(x - 3)?

Back

The standard form is y = x^2 - 2x - 3.

Front

Identify the zeros of the polynomial y = (x + 4)(x + 1)(x - 3).

Back

The zeros are -4, -1, and 3.

Front

What are the three factors of (x^3 + 7x^2 + 7x - 15) ÷ (x - 1)?

Back

The factors are (x - 1)(x + 5)(x + 3).

Front

Define 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

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial.

Front

Explain what a factor of a polynomial is.

Back

A factor of a polynomial is a polynomial that divides the original polynomial without leaving a remainder.

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that if a polynomial f(x) is divided by (x - c), the remainder is f(c).

Front

What is 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.