Question

Complete the factorization of 3x ^ 2 - 10x + 8 3x^ 2 -10x+8=(x- Box x-4)

Answer 1

`3x^2-10x+8=(x-x_1)(x-x_2)=(x-2)(x-(4)/(3))`

Explanation:

The general form of a quadratic polynomial is given by:

`ax^2+bx+c` (1)

You have the following polynomial:

`3x^2-10x+8` (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:

`x_(1,2)=(-b\pm √(b^2-4ac))/(2a)` (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):

`x_(1,2)=(-(-10)\pm √((-10)^2-4(3)(8)))/(2(3))\\\\x_(1,2)=(10\pm2)/(6)\\\\x_1=2\\\\x_2=(4)/(3)`

Then, the factorization of the polynomial is:

`3x^2-10x+8=(x-x_1)(x-x_2)=(x-2)(x-(4)/(3))`