The factorization of p(x) = 2x³ - 2x² - 3x is written as:
p(x) = x*(x - (1/2)*(1 + √7))*(x - (1/2)*(1 - √7))
How to factorize the polynomial?
Here we have the polynomial:
p(x) = 2x³ - 2x² - 3x
First, we can take the common factor x to get:
p(x) = (2x² - 2x - 3)*x
Now we can factorize the quadratic polynomial:
We need to solve:
2x² - 2x - 3 = 0
The solutions are given by:
[tex]x = \frac{2 \pm \sqrt{(-2)^2 - 4*(-3)*2} }{2*2} \\\\x = \frac{2 \pm 2\sqrt{7} }{4}[/tex]
So the two solutions are:
x = (1/2)*(1 + √7)
x = (1/2)*(1 - √7)
Then the factorized polynomial is:
p(x) = x*(x - (1/2)*(1 + √7))*(x - (1/2)*(1 - √7))
If you want to learn more about factorization:
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