# 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,

a

_{n}x_{n}+ a_{n-1}x^{n-1}+ a_{n-2}x^{n-2}+ … + a_{2}x^{2}+ a_{1}x + a_{0}= 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 x

^{3}– 4x^{2}+ 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)(x

^{2}– 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 2x

^{3}– 9x^{2}+ 3x + 1 = 0, then specify the other roots.
Answers:

Thus, the form of the equation becomes
(x – ½)(2x

^{2}– 8x – 2) = 0.
for 2x

^{2}– 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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