Answer:
The other factor is 4x-3
Explanation:
We want to divide 4x^2 + 5x -6 by x + 2
Unfortunately, we cannot say if x + 2 is a factor or not.
To know if it’s,
we set x + 2 = 0 and this means x = -2
We substitute this into the larger polynomial.
This gives;
4(-2)^2 + 5(-2) -6 = 16 -10-6 = 0
What this actually means is that it is a factor of it since it leaves no remainder.
The issue now is finding this other factor.
So let’s use the long division
(x + 2). _| 4x ^2 + 5x -6
Kindly note that 4x^2/x = 4x, we now multiply this by (x+2) so we get 4x(x+2) = 4x^2 + 8x which we will subtract from 4x^2 + 5x -6
_ 4x_
(x+2). ___|4x^2 + 5x -6
-(4x^2 + 8x)
-3x -6
next is -3x/x = -3
_-4x-3_
(x+2). _| 4x^2 + 5x-6
-(4x^2 +8x)
__________
-3x-6
-(-3x-6)
_________
0
So the other factor is 4x-3