RTCNTC said:Precalculus by David Cohen, 3rd Edition
Chapter 1, Section 1.3.
Question 44b.
Factor the expression.
x^3 + 2x^2 + x
x(x^2 + 2x + 1)
x(x + 1)(x + 1)
x(x + 1)^2
Correct?
A cubic function is a type of polynomial function with a degree of 3. It is written in the form f(x) = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants.
To graph a cubic function, you can plot points by choosing values for x and solving for corresponding values of y. You can also use transformations, such as shifting and reflecting, to graph the function.
The factor theorem states that if a polynomial function f(x) has a root x = c, then (x - c) is a factor of f(x). This means that if you can find a value of x that makes the polynomial equal to 0, then you can factor out (x - c) from the polynomial.
To factor a cubic function, you can use the factor theorem to find one root, and then use long or synthetic division to divide the polynomial by (x - c). This will leave you with a quadratic expression, which you can then factor using methods such as the quadratic formula or completing the square.
The roots of a cubic function are the values of x that make the function equal to 0. The factors of a cubic function are expressions that can be multiplied together to get the original function. The roots of a cubic function are also the values of x that make the factors equal to 0.