Answer:
[tex]3x^2-10x+8=(x-x_1)(x-x_2)=(x-2)(x-\frac{4}{3})[/tex]
Step-by-step explanation:
The general form of a quadratic polynomial is given by:
[tex]ax^2+bx+c[/tex] (1)
You have the following polynomial:
[tex]3x^2-10x+8[/tex] (2)
In order to complete the factorization you can use the quadratic formula, to obtain the roost of the polynomial. The quadratic formula is given by:
[tex]x_{1,2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex] (3)
By comparing the equation (1) with the equation (2) you obtain:
a = 3
b = -10
c = 8
Then, you replace these values in the equation (3):
[tex]x_{1,2}=\frac{-(-10)\pm \sqrt{(-10)^2-4(3)(8)}}{2(3)}\\\\x_{1,2}=\frac{10\pm2}{6}\\\\x_1=2\\\\x_2=\frac{4}{3}[/tex]
Then, the factorization of the polynomial is:
[tex]3x^2-10x+8=(x-x_1)(x-x_2)=(x-2)(x-\frac{4}{3})[/tex]
