Factoring Polynomials

Front

What is the formula for factoring the sum of cubes, a³ + b³?

Back

(a + b)(a² - ab + b²)

Front

What is the formula for factoring the difference of cubes, a³ - b³?

Back

(a - b)(a² + ab + b²)

Front

How do you factor the polynomial 2x⁴ - 13x² - 70?

Back

(2x² + 7)(x² - 10)

Front

What is the factored form of 8x³ - 1?

Back

(2x - 1)(4x² + 2x + 1)

Front

How do you factor the polynomial 7r³ - 8r² + 42r - 48?

Back

(r² + 6)(7r - 8)

Front

What is the first step in factoring a polynomial?

Back

Look for a common factor in all terms.

Front

What is the significance of the difference of squares in factoring?

Back

It allows you to factor expressions of the form a² - b² into (a - b)(a + b).

Front

What is a polynomial?

Back

A mathematical expression consisting of variables, coefficients, and non-negative integer exponents.

Front

What does it mean to factor a polynomial?

Back

To express it as a product of its factors.

Front

What is the role of the leading coefficient in polynomial factoring?

Back

It affects the shape and direction of the polynomial's graph.