Graphing, Factoring & Solving Cubic Functions

Front

What is a cubic function?

Back

A cubic function is a polynomial function of degree three, typically expressed in the form f(x) = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants and a ≠ 0.

Front

What does it mean to factor a polynomial?

Back

Factoring a polynomial involves expressing it as a product of its factors, which are polynomials of lower degrees.

Front

What is the difference of cubes formula?

Back

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

Front

What is the sum of cubes formula?

Back

The sum of cubes formula states that a^3 + b^3 = (a + b)(a^2 - ab + b^2).

Front

How do you factor x^3 - 64?

Back

Using the difference of cubes formula: x^3 - 4^3 = (x - 4)(x^2 + 4x + 16).

Front

What is the first step in factoring 2x^4y - 54xy?

Back

Factor out the greatest common factor (GCF), which is 2xy, resulting in 2xy(x^3 - 27).

Front

What is the factored form of 8u^3 + 27?

Back

Using the sum of cubes formula: 8u^3 + 27 = (2u + 3)(4u^2 - 6u + 9).

Front

What is the process of multiplying two binomials?

Back

Use the distributive property (FOIL method): Multiply the first terms, outer terms, inner terms, and last terms, then combine like terms.

Front

What is the result of (3x - 4)(4x + 5)?

Back

The result is 12x^2 - x - 20.

Front

What is the significance of the leading coefficient in a cubic function?

Back

The leading coefficient determines the end behavior of the graph of the cubic function.