Final answer:
To simplify (4x^3+23x^2+22x-10)(x+2)^-1, we divide the polynomial by x+2 and find the equivalent expression is D) 4x^2+15x-8-6/(x+2).
Step-by-step explanation:
The expression (4x^3+23x^2+22x−10)(x+2)^-1 can be simplified by polynomial long division or synthetic division, as it involves dividing a polynomial by a binomial. To find the equivalent expression, we divide the polynomial 4x^3+23x^2+22x−10 by x+2, keeping in mind that a negative exponent denotes division. We look for the quotient that, when multiplied by (x+2), gives us the original polynomial as closely as possible, with any remainder becoming a fraction over (x+2). The equivalent expression obtained through this division process will be a polynomial with a possible fractional term where the remainder is over (x+2). After performing the division, we find that the correct answer is D) 4x^2+15x−8−6/(x+2).