when 7x^4-49x^3+7x^2 is divided by 7x^2, the quotient is
when I divided I got
x^2-7x+1
Is this correct?
yes. good work.
Yes, your answer is correct! To double-check the division, let me explain the process step by step:
When dividing the polynomial 7x^4 - 49x^3 + 7x^2 by 7x^2, you should follow these steps:
1. Divide the first term of the dividend (7x^4) by the divisor (7x^2).
7x^4 / 7x^2 = x^2.
2. Multiply the result from step 1 (x^2) by the whole divisor (7x^2).
x^2 * 7x^2 = 7x^4.
3. Subtract the result from step 2 (7x^4) from the original dividend (7x^4 - 49x^3 + 7x^2).
(7x^4 - 49x^3 + 7x^2) - 7x^4 = -49x^3 + 7x^2.
4. Bring down the next term from the original dividend (7x^2).
-49x^3 + 7x^2.
5. Repeat steps 1-4 with the new expression (-49x^3 + 7x^2).
Following these steps, we divide -49x^3 + 7x^2 by 7x^2:
1. (-49x^3) / (7x^2) = -7x.
2. -7x * 7x^2 = -49x^3.
3. (-49x^3 + 7x^2) - (-49x^3) = 7x^2.
Now, we have completed the division. The quotient is x^2 - 7x + 1. So, you were correct in your division!