How do you find polynomial function when given the factors?

Answer 1

Multiply the factors together to get the function itself.

You'll need to use basic distributive properties to multiply factors:

a(b+c) = ab + ac

(a+b)(c+d) = ac+ad+bc+bd

As a simple example,

(1+2)(3+4) = 1*3 + 1*4 + 2*3 + 2*4 = 3*7 = 21

Now, apply this to your factors, which are often given in the form (x+c).

For instance, given the following two factors of the function f(x), find the function:

Factors: (x+2), (x+3), x

1.Define the function as a product of its factors

f(x) = x(x+2)(x+3)

2. multiply the two binomial factors

f(x) = x*(x*x + x*3 + 2*x + 2*3)

3. multiply the result by the remaining factor (x)

f(x) = x*x*x + x*x*3 + x*x*2 + x*2*3

4.simplify the result

f(x) = x3 + 5x2 + 6x