Question

Please Help!!!Use division and factoring / the quadratic formula to solve the equation from the given factor. x^3-49x-120=0; (x+5)

Answer 1

x^3-49x-120=0

then

x^3 - 49x = 120

now factorize

x• (x^2 - 49) = 120

factorze again using a^2 - b^2 = (a+b)•(a-b)

x• (x-7)•(x+7 ) = 120

Now divide

x^3 - 49x - 120. |__x + 5

. -5x^2 -49x x^ 2- 5x -24

. +25x

. -24x - 120

. 0

Then equation is transformed to

(x+5)• (x^ 2- 5x -24) = 0

Now find solutions of

x^ 2- 5x -24= 0 by completing square

x = --5/2 ± [ √ (25 - 4•-24) ]/2

. = 5/2 ± √ 121/ 2

. = 5/2 ± 11/2

Then solutions are x= (5+11)/2 = 8

and. x = (5-11)/2 = -3

Then answer is

Solutions x= -5, 8 , -3

.