I am having problems with polynomial functions.
f(x)= (x-3)(x+2)(x+4)
are you just wanting to multiply them together? if so, just do the first 2 first. FOIL. First, Outside, Inside, Last. F: x*x=x^2. O: x*2=2x. I: -3*x=-3x. L: -3*2=-6. Then you add all of those together. So you get: x^2-x-6. Now you have to multiply the third part. So you have (x+4)(x^2-x-6). So multiply the x through everything, and then the 4 through everything, and then add it all together. So x*x^2=x^3. x*-x=-x^2. x*-6=-6x. 4*x^2=4x^2. 4*-x=-4x. 4*-6=-24. So now you have to add all of these numbers together. So add: x^3 + -x^2 + -6x + 4x^2 + -4x + -24. combine like terms and you should get: x^3 + 3x^2 - 10x - 24 as your final answer. I really hope this helped!!!
(x - 3) (x + 2) (x + 4)
Multiply the 1st term in the 1st
parenthesis by each term in the 2nd
parenthesis. Then multiply the 2nd term
in the 1st parenthesis by each term in
2nd parenthesis.
(x^2 + 2x - 3x - ) (x + 4)=
Combine like-terms in 1st parentthesis:
(x^2 -x -6) (x + 4)=
Multiply the 1st term in 1st par. by
each term in 2nd par. Then multiply
2nd term in 1st par. by each term in
2nd par.
x^3 + 4x^2 - x^2 - 4x -6x -24 =
Combine like-terms:
x^3 + 3x^2 - 10x -24.
Polynomial functions can sometimes be challenging, but I'm here to help you understand them better. The given polynomial function is f(x) = (x-3)(x+2)(x+4). This is an example of a polynomial of degree 3, also known as a cubic function.
To solve problems related to polynomial functions, it's helpful to know a few key concepts:
1. Polynomial Degree: The degree of a polynomial is the highest exponent or power of x in the polynomial. In this case, the degree is 3 because the highest exponent of x is 3.
2. Factoring: Factoring a polynomial involves expressing it as a product of simpler polynomials or linear factors. In the given polynomial, it is already factored as (x-3)(x+2)(x+4).
To evaluate the polynomial function, you can substitute a specific value for x and perform the necessary calculations. For example:
To find the value of f(x) when x = 1, substitute it in the expression:
f(1) = (1-3)(1+2)(1+4)
= (-2)(3)(5)
= -30
So, when x = 1, f(x) equals -30.
You can also find the x-intercepts or roots of the polynomial by setting f(x) equal to zero and solving for x. In this case, it means finding the values of x when the polynomial equals zero.
To find the x-intercepts, set f(x) = 0:
(x-3)(x+2)(x+4) = 0
To find the solutions, you can set each factor equal to zero and solve for x:
x-3 = 0 ==> x = 3,
x+2 = 0 ==> x = -2,
x+4 = 0 ==> x = -4.
So, the x-intercepts or roots of f(x) are x = 3, x = -2, and x = -4.
These are some ways to deal with polynomial functions. If you have any more specific questions or need further assistance, feel free to ask!