Question

What is the quotient when ((28x^7 + 21x^6 - 42x^2)) is divided by (-7x^2)?

Answer 1

The quotient of ((28x^7 + 21x^6 - 42x^2)) divided by (-7x^2) is -4x^5 - 3x^4 + 6.

Step-by-step explanation:

The student has asked what quotient is obtained when the polynomial ((28x^7 + 21x^6 - 42x^2)) is divided by the monomial (-7x^2). This is an algebraic operation involving polynomial division. To find the quotient, we divide each term of the polynomial by the monomial.

Here are the steps to divide the polynomial by the monomial:

1. Divide the first term of the polynomial (28x^7) by (-7x^2) to get -4x^5.
2. Divide the second term (21x^6) by (-7x^2) to get -3x^4.
3. Finally, divide the last term (-42x^2) by (-7x^2) to get 6.

The quotient is therefore -4x^5 - 3x^4 + 6.