All the real zeros of the given polynomial are integers. Find the zeros and write the polynomial in factored form. X^3+2x^2-13x+10
To find the zeros of the polynomial, we can try plugging in integers as potential solutions and see if they make the polynomial equal to zero.
By testing a few integers, we find that x = -2 is a zero of the polynomial.
Since -2 is a zero of the polynomial, we know that (x + 2) is a factor of the polynomial.
To find the remaining factors, we can use polynomial division or synthetic division. Dividing the polynomial by (x + 2), we get:
x^2 - 7x + 5
Now, we need to find the zeros of the new polynomial x^2 - 7x + 5.
By factoring or using the quadratic formula, we find that the zeros are x = 1 and x = 5.
Therefore, the zeros of the original polynomial x^3 + 2x^2 - 13x + 10 are x = -2, x = 1, and x = 5.
To write the polynomial in factored form, we can write it as:
(x + 2)(x - 1)(x - 5)