Cubic Functions Review

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 is the general form of a cubic function?

Back

The general form of a cubic function is f(x) = ax^3 + bx^2 + cx + d.

Front

How do you find the zeros of a polynomial?

Back

To find the zeros of a polynomial, set the polynomial equal to zero and solve for x.

Front

What does it mean for a point to be a zero of a polynomial?

Back

A point (x, 0) is a zero of a polynomial if substituting x into the polynomial results in zero.

Front

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

Back

The leading coefficient (the coefficient of x^3) determines the end behavior of the cubic function and whether it opens upwards or downwards.

Front

What is the relationship between the degree of a polynomial and the number of zeros it can have?

Back

A polynomial of degree n can have at most n real zeros.

Front

How do you multiply two polynomials?

Back

To multiply two polynomials, use the distributive property (FOIL for binomials) to multiply each term in the first polynomial by each term in the second polynomial.

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 difference between a linear function and a cubic function?

Back

A linear function has a degree of 1 and graphs as a straight line, while a cubic function has a degree of 3 and can have a more complex shape with up to 3 turning points.

Front

What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a linear divisor of the form (x - c).