Flashcard 4.4/4.5 - Factoring and solving polynomial equations

Front

What is the difference of cubes formula?

Back

The difference of cubes formula is: a^3 - b^3 = (a - b)(a^2 + ab + b^2).

Front

Factor the difference of cubes: x^3 - 343.

Back

(x - 7)(x^2 + 7x + 49).

Front

What are the zeros of a polynomial?

Back

The zeros of a polynomial are the values of x that make the polynomial equal to zero.

Front

Find the zeros of the polynomial: f(x) = (x-5)(2x+3)(7x-4)(x+6).

Back

x = 5, -\frac{3}{2}, \frac{4}{7}, -6.

Front

How many zeros does a polynomial of degree n have?

Back

A polynomial of degree n has exactly n zeros, counting multiplicities.

Front

What is the relationship between the degree of a polynomial and its zeros?

Back

The degree of a polynomial indicates the maximum number of zeros it can have.

Front

Identify a polynomial equation from its zeros: 3, -1, 5.

Back

g(x) = (x - 3)(x + 1)(x - 5).

Front

What is the factored form of a polynomial?

Back

The factored form of a polynomial expresses it as a product of its linear factors.

Front

What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient determines the end behavior of the polynomial graph.

Front

How do you find the zeros of a polynomial function?

Back

Set the polynomial equal to zero and solve for x.