What is the solution to the division problem below? (You can use long division or synthetic division.) (4x2 + 5x - 6) (x + 2)

The other factor is 4x-3

Step-by-step 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

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step-by-step explanation: