The quotient of \((x^4 + 7x^3 + 28x - 16)\) and a polynomial is \((x^2 + 7x - 4)\). What is the polynomial?

A. \(x^2 + 4\)
B. \(x^2 - 4\)
C. \(x^6 + 14x^5 + 45x^4 + 180x^2 + 224x + 64\)
D. \(x^6 + 14x^5 + 45x^4 + 180x^2 - 224x + 64\)

By multiplying the provided quotient, (x^2+7x-4), with each of the answer choices, we can find the polynomial that, when divided, results in the given quotient.

Explanation:

To find the polynomial that when divided into (x4+7x3+28x-16) results in (x2+7x-4), we can perform polynomial division, also known as long division of polynomials. If we divide the given polynomial by the quotient, we'll reveal the missing polynomial that represents the divisor.

Normally, the process of long division would be carried out to find the divisor, but as this is a multiple-choice question, we can simply multiply the provided quotient by each of the answer choices to see which product matches the original polynomial.

The quotient of \((x^4 + 7x^3 + 28x - 16)\) and a polynomial is \((x^2 + 7x - 4)\). What is the polynomial?A. \(x^2 + 4\) B. \(x^2 - 4\) C. \(x^6 + 14x^5 + 45x^4 + 180x^2 + 224x + 64\) D. \(x^6 + 14x^5 + 45x^4 + 180x^2 - 224x + 64\)

Answer :

Final answer:

Explanation:

Other Questions

The quotient of \((x^4 + 7x^3 + 28x - 16)\) and a polynomial is \((x^2 + 7x - 4)\). What is the polynomial?

A. \(x^2 + 4\)
B. \(x^2 - 4\)
C. \(x^6 + 14x^5 + 45x^4 + 180x^2 + 224x + 64\)
D. \(x^6 + 14x^5 + 45x^4 + 180x^2 - 224x + 64\)