Final answer:
To divide x³-6 by x+2, use long division. The result is x²-2x+4 with a remainder of -14.
Step-by-step explanation:
To divide x³-6 by x+2, we can use long division.
Step 1: Divide the first term x³ by x to get x.
Step 2: Multiply x+2 by x² to get x³+2x². Su²btract this from the dividend: x³- (x³+2x²) which gives -2x².
Step 3: Bring down the next term -6. Divide -2x² by x to get -2x. Multiply x+2 by -2x to get -2x²-4x. Subtract this from the previous result: -2x²- ( -2x²-4x) which gives 4x.
Step 4: Divide 4x by x to get 4. Multiply x+2 by 4 to get 4x+8. Subtract this from the previous result: 4x- (4x+8) which gives -14.
Therefore, the result of dividing x³-6 by x+2 is x²-2x+4 with a remainder of -14.