Question

Use the graph of the 3rd degree polynomial and one factor to write the factored form of the polynomial suggested by the graph Factor is (x^2+x+1)Y=

Answer 1

y = (x^2 + x + 1) ( x - 5)

Step-by-step explanation:

We already know that one factor of the polynomial is (x^2 + x + 1), we just need to find the second factor.

How do we know that the polynomial has only two factors, though? Because we are told that the polynomial is 3rd degree and therefore, we need to multiply (x^2 + x + 1) by "one x term" to get a third-degree polynomial.

Now, what might our unknown factor be?

Well, looking at the graph we see that the polynomial has a zero at x = 5; therefore, its factorization must contain the term x - 5; therefore, we conclude that the factored form of the polynomial must be

`y=(x^2+x+1)(x-5)`

which is our answer!

Note: if you plot y = (x^2 + x + 1)(x - 5) you will get exactly the same graph as shown in the question.