# How to Find the Remaining Factors When Given One Factor

Brian McLogan
Published at : 22 Nov 2020
15976 views
138
9

Learn how to find all the zeros of a polynomial given one rational zero. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The zeros of a polynomial are the values of x for which the value of the polynomial is zero.

To find the zeros of a polynomial when one of the zeros is known, we use synthetic division to divide the polynomial with the given zero or we use long division to divide the polynomial with the given zero expressed in factor form. This gives the other factor of the polynomial, which can be further factored (if need be) using any of the techniques for factoring polynomials.

After we have factored the polynomial, we can then use the zero-product property to evaluate the factored polynomial and hence obtain the remaining zeros of the polynomial. Recall that the zero-product property states that when the product of two or more terms is zero, then either of the term is equal to 0.
#polynomials #givenfactorzero