Question

How do you find the x-intercepts if given the following polynomial in factored form?

X(x-2)^2(x+4)(x+1)​

Answer 1

Explanation:

You know the intercepts occur at x = 0, so set each part of the factored form equal to zero and solve for x.

The first part, plain X = 0, so X = 0 is a root, an x-intercept

The second part (X-2)^2 = 0, so X = 2 is another root. Since the function is being squared, this root will happen twice. The function crosses this root twice.

The third part (x+4) = 0, so x = -4 is another root.

Finally, (x+1) so x = -1 is another root.

So you have X = 0, X = 2, X = -4, X = -1 as your x-intercepts