Final answer:
The quotient when dividing the polynomial (28x^7 + 21x^6 - 42x^5) by -7x^2 is -4x^5 - 3x^4 - 6x^3, applying standard polynomial division rules and sign division rules.
Step-by-step explanation:
To determine the quotient of the given polynomial (28x? + 21x6 - 42x?) when it is divided by -7x2, we apply polynomial division, similarly to how we would divide numbers. We align terms with like degrees and divide each term by -7x2, taking care of the sign rules for division.
First, let's correct any typos in the expression. It seems there are some question marks instead of the actual exponents, but assuming the pattern follows from the second term which is 21x6, we can infer that the other terms could be 28x7 and 42x5. Dividing each term of the polynomial by -7x2, we get:
- 28x7 / (-7x2) = -4x5
- 21x6 / (-7x2) = -3x4
- 42x5 / (-7x2) = -6x3
So the quotient is -4x5 - 3x4 - 6x3.
Additionally, understanding the rule behind subtraction of exponents during division is key, as demonstrated in equation 256 × 10-38 ÷ 5 × 10-21 = 1,024 × 10-18, where similar exponent bases are subtracted when divided.