Question

Factor the following trinomial. (Hint: Solve the equations first.)

x²-2x-2

Answer 1

Explanation:

Answer 2

`(x-(1+√(3)))(x-(1-√(3)))`

Explanation:

we know that

The formula to solve a quadratic equation of the form

`ax^(2) +bx+c=0`

is equal to

`x=\frac{-b(+/-)\sqrt{b^(2)-4ac}} {2a}`

in this problem we have

`x^(2) -2x-2=0`

so

`a=1\\b=-2\\c=-2`

substitute in the formula

`x=\frac{-(-2)(+/-)\sqrt{-2^(2)-4(1)(-2)}} {2(1)}`

`x=\frac{2(+/-)√(12)} {2}`

`x=\frac{2(+/-)2√(3)} {2}`

`x_1=\frac{2(+)2√(3)} {2}=1+√(3)`

`x_2=\frac{2(-)2√(3)} {2}=1-√(3)`

therefore

`x^(2) -2x-2=(x-(1+√(3)))(x-(1-√(3)))`