Adv Algebra Practice Flashcard: Factor and Solve Polynomials

Front

What is the difference between factoring and solving a polynomial?

Back

Factoring a polynomial involves expressing it as a product of its factors, while solving a polynomial involves finding the values of the variable that make the polynomial equal to zero.

Front

What is the factored form of a difference of cubes, such as x³ - a³?

Back

The factored form is (x - a)(x² + ax + a²).

Front

How do you factor a polynomial of the form x³ + a³?

Back

Use the formula: x³ + a³ = (x + a)(x² - ax + a²).

Front

What are the steps to factor a polynomial completely?

Back

1. Look for a common factor. 2. Use special factoring formulas (difference of squares, sum/difference of cubes). 3. Factor by grouping if applicable. 4. Continue factoring until no further factoring is possible.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is written in descending order of the degree of its terms, such as f(x) = ax^n + bx^(n-1) + ... + k.

Front

How do you find the zeros of a polynomial?

Back

Set the polynomial equal to zero and solve for the variable using factoring, the quadratic formula, or other methods.

Front

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

Back

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

Front

What is the factored form of the polynomial x³ - 27?

Back

(x - 3)(x² + 6x + 9).

Front

How do you write a polynomial given its zeros?

Back

Use the zeros to create factors of the form (x - zero) and multiply them to form the polynomial.

Front

What is the significance of the Rational Root Theorem in polynomial equations?

Back

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