Question

the graph of each function is shown. write the function in factored form . do not include complex numbers

Answer 1

We can see from the picture that the function f(x) has roots in x = -5 and x = 5. Using sintetic division with x = 5, we get:

then, we can write the function as:

$f(x)=(x-5)(2x^3+11x^2+8x+15)$

since we know that another root is x = -5,we can use again the sintetic division on the right factor:

therefore, the function in factored form is:

$f(x)=(x-5)(x+5)(2x^2+x+3)$