use long division
1.2x3+3x2-17x+1 /x-2
2.y3+3y2+1 /y-2
3.n5-n2 /n2-n
Sure! I can help you with long division for these three problems. Let's go through each of them step by step.
1.2x^3 + 3x^2 - 17x + 1 / (x - 2):
Step 1: Start by dividing the highest degree term in the numerator by the highest degree term in the denominator. In this case, divide 1.2x^3 by x to get 1.2x^2.
Step 2: Multiply the divisor (x - 2) by 1.2x^2, which gives you 1.2x^3 - 2.4x^2.
Step 3: Subtract this result from the original numerator: (1.2x^3 + 3x^2 - 17x + 1) - (1.2x^3 - 2.4x^2) = 5.4x^2 - 17x + 1.
Step 4: Repeat steps 1-3 with the simplified numerator (5.4x^2 - 17x + 1) until the degree of the numerator is less than the degree of the denominator.
Continuing the process will give you the final result.
2. y^3 + 3y^2 + 1 / (y - 2):
Follow the same steps as mentioned above for this problem as well.
3. n^5 - n^2 / (n^2 - n):
Again, apply the same steps as above to find the solution.
Remember to simplify the expressions after each step and continue the process until the degree of the numerator is less than the degree of the denominator.