Question

I NEED HELP PLS THIS IS DUE IN 3 HOURS

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

x^2−2x−2

and

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

x2−6x+4

(these are 2 different problems pls HELP!)

Answer 1

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

Part 2)
`x^(2) -6x+4=(x-3-√(5))(x-3+√(5))`

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}`

Part 1)

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)))`

`x^(2) -2x-2=(x-1-√(3))(x-1+√(3))`

Part 2)

in this problem we have

`x^(2) -6x+4=0`

so

`a=1\\b=-6\\c=4`

substitute in the formula

`x=\frac{-(-6)(+/-)\sqrt{-6^(2)-4(1)(4)}} {2(1)}`

`x=\frac{6(+/-)√(20)} {2}`

`x=\frac{6(+/-)2√(5)} {2}`

`x_1=(6(+)2√(5))/(2)=3+√(5)`

`x_2=(6(-)2√(5))/(2)=3-√(5)`

therefore

`x^(2) -6x+4=(x-(3+√(5)))(x-(3-√(5)))`

`x^(2) -6x+4=(x-3-√(5))(x-3+√(5))`