Solving Polynomial by Factoring Equations

When you solve quadratic equations, one way to solve it is by factoring the form. The principle used is the following multiplication.

If a . b = 0 then a = 0 or b = 0

Similarly, for the following polynomial equations,, untuk persamaan polinomial berikut ini,

anxn + an-1xn-1 + an-2xn-2 + … + a2x2 + a1x + a0 = 0

The principle used is not different from the principle in solving quadratic equations. The method of solving polynomial equations is only by factoring. Because the polynomial equation does not have a special formula as in the quadratic equation.

Example 1.
Determine the set of completion equations x3 – 4x2 + x + 6 = 0.
Answers:
By experimenting with several factors from 6 such as ± 1, ± 2, ± 3 and ± 6, we find the remainder of the division 0 for x = -1, i.e.


So that the form of the equation changes to the equation below,
(x + 1)(x2 – 5x + 6) = 0
(x + 1)(x – 2)(x – 3) = 0
X = -1 or x = 2 or x = 3

so, the solution is {-1, 2, 3}.

Example 2.
If ½ is one of the square roots of the equation 2x3 – 9x2 + 3x + 1 = 0, then specify the other roots.
Answers:

Thus, the form of the equation becomes (x – ½)(2x2 – 8x – 2) = 0.

for 2x2 – 8x – 2 equations cannot be factored, so to solve them only by using the quadratic formula (abc formula) as follows,

So, the other roots are 2 + √5 and 2 - √5.



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