Pls help answer this, 10 pnts ryt away. for those who loves math.xD?

Question

Factor the polynomial.

1.) By completing the square.

a.) X2-6x-2

2) Using synthetic division.

a.) a4-2a3-3a2+4a+4

Answer 1

Factor by completing the square

x^2 - 6x - 2 = 0

Constant must be in the right side.

x^2 - 6x = 2

Divide the coefficient of x by 2 and square it.

Coefficient of x is -6, divided it by 2 ==> -6/2 = -3 and square it ==>  

-3^2 = 9

Add the answer to both sides

x^2  - 6x + 9 = 2 + 9

x^2 - 6x + 9 = 11

(x - 3 )^2 = 11

Take square root of both sides

x - 3 =  +/- sqrt 11

x =  3 + sqrt 11 =  3 + 3.3166 = 6.3166

x =  3 - sqrt 11 =  3 - 3.3166 = -0.3166

2) Using sythethic division.

a^4 -2a^3 - 3a^2 + 4a + 4

I cannot show it here but take x-2 and x+ 1 as a factor.

It will go into this ==>

( x - 2) (x + 1) ( x - 2) (x + 1) = 0

x = 2 and - 1

Answer 2

x^2 - 6x - 2 = 0

x^2 - 6x = 2

x^2 - 6x + 9 = 2 + 9

(x-3)^2 = 11

x - 3 = ±sqrt(11)

x = ±sqrt(11) + 3

____ (a^3 - 3a^2  +  0a + 4)

(a^4 - 2a^3 - 3a^2 + 4a + 4) divided by (a+1)

a^4 + a^3

__ - 3a^3 - 3a^2 + 4a + 4

__ - 3a^3 - 3a^2

_______________ 4a + 4

_______________ 4a + 4

_____ (a^2 - 4a + 4)

(a^3 - 3a^2 + 0a + 4) divided by (a+1)

a^3 + a^2

___ -4a^2 + 0a + 4

___  -4a^2 - 4a

_________ 4a + 4

_________ 4a + 4

____ (a   - 2)

(a^2 - 4a + 4) divided by (a-2)

a^2 - 2a

____ -2a + 4

____ -2a + 4

sorry, the formatting is so ugly... but the division gives the factorization:

(x+1)^2 * (x-2)^2

Answer 3

1)

x^2 - 6x - 2  = x^2 - 6x + (6/2)^2 - (6/2)^2 - 2

= x^2 - 6x + 9 - 11

= (x-3)^2 - 11

= (x - 3 - sqrt(11)) . (x  -3 + sqrt(11))

2)

a^4 - 2a^3 - 3a^2 + 4a + 4 = a^2 . (a^2 - 2a - 3) + 4(a + 1)

= a^2 . (a+1)(a-3) + 4(a+1)

= (a+1). (a^3 - 3a^2 + 4)

It's easy to see that -1 is a root of a^3 - 3a^2 + 4

then, dividing it by (a+1) we get

a^3 - 3a^2 + 4 = (a+1) . (a^2 - 4a + 4) = (a+1) . (a-2)^2

Then

a^4 - 2a^3 - 3a^2 + 4a + 4 = (a+1) . (a+1) . (a-2)^2 = (a+1)^2 . (a+2)^2