Question

given that x=-1 is a root of g(x)=2x^3-5x^2-x+6, completely factor

Answer 1

Do you know synthetic division? If you do, take the root they gave you - x = -1 - and then used that to find the other roots. Based off the 2x^3 we know that there will be 2 more roots.

Answer 2

Yes I did synthetic division, and got 2x^2-7x+6 with remainder of 0

Answer 3

Okay that's right, so now you should factor by either completing the square or quadratic formula

Answer 4

ok well I factored by grouping and got
2x^2-7x+6
(2x^2-3x)(-4x+6)
x(2x-3)-2(2x-3)

Answer 5

@EmergencyExit

Answer 6

@Nnesha

Answer 7

if you think of (2x-3) as "one thing" (and it is)
then
x(2x-3)-2(2x-3)
is like the problem
xy-2y
where you factor y from each term to get (x-2)y

but in your problem, we factor out (2x-3)
x(2x-3)-2(2x-3) = (x-2)(2x-3)

that means g(x) in factored form is
(x+1)(x-2)(2x-3)

Answer 8

@phi You can completely simplify 2x-3 by setting it as an equation equal to 0.
2x-3=0
+ 3 +3
2x = 3
x = 3/2