Example: 3x3 – 4x2 – 17x + 6
Now we put these numbers in a chart to find all the possible combinations of these factors in the form b/c. Where the constant term (6) is the “b” and the coefficient of the first term (3) is the “c”.
List the factors of the “b” term along the top, with a ± sign in front of each number.
List the factors of the “c” term on the left side, with a ± sign in front of each number.
±1 ±2 ±3 ±6 (ßb’s : the factors of 6) factors of 3: ±1 ± ± ± ± the c’s ±3 ± ± ± ±
±1 ±2 ±3 ±6 ±1 ±1 ±2 ±3 ±6 ±3 ± ± ±1 ±2
Finding the zeros/linear factors of a polynomial: (b/c part 2) College Algebra
To find the zeros of a polynomial we will first find all the possible factors of the polynomial in the form b/c. We will assume that we have already found these for the following polynomial.
Example: 3x3 – 4x2 – 17x + 6
All the possible factors are: ±1 ±2 ±3 ±6 ±1/3 ± 2/3
Now we put these numbers in a chart and use synthetic division to find the value of the remainder. Stop when you get a remainder equal to zero.
List the factors on the left side, with a + sign and then a – sign in front of each number.
Now use synthetic division until we find the first remainder equal to zero.
3 -4 -17 6 (ßthe coefficients of the polynomial) +1 3 -2 -18 -12 -1 3