Find a polynomial of degree 3 with real coefficients and zeros calculator

A polynomial of degree 3 has three roots and thus must be of the form a(x−r1)(x−r2)(x−r3) . We are given the roots −3 , −1 , and 4 . Thus, we just need to substitute these as r1 , r2 , and r3 . This gives us a(x+3)(x+1)(x−4) .

How To: Given a factor and a third-degree polynomial, use the Factor Theorem to factor the polynomial. Use synthetic division to divide the polynomial by (x−k) . Confirm that the remainder is 0. Write the polynomial as the product of (x−k) and the quadratic quotient.