Which of the following polynomials has a remainder -43 of when divided by x + 3?Group of answer choices𝑥3+2𝑥2+10𝑥+4𝑥3+2𝑥2+10𝑥−4𝑥3−2𝑥2+10𝑥+4

To find out which polynomial has a remainder of -43 when divided by x + 3, we can use the Remainder Theorem. The Remainder Theorem states that if a polynomial f(x) is divided by x - k, the remainder is f(k).

In this case, we are dividing by x + 3, so we can set k = -3.

We substitute -3 into each polynomial and find the one that gives us -43.

1. For the polynomial 𝑥3+2𝑥2+10𝑥+4: (-3)^3 + 2*(-3)^2 + 10*(-3) + 4 = -27 + 18 - 30 + 4 = -35

2. For the polynomial 𝑥3+2𝑥2+10𝑥−4: (-3)^3 + 2*(-3)^2 + 10*(-3) - 4 = -27 + 18 - 30 - 4 = -43

3. For the polynomial 𝑥3−2𝑥2+10𝑥+4: (-3)^3 - 2*(-3)^2 + 10*(-3) + 4 = -27 - 18 - 30 + 4 = -71

So, the polynomial 𝑥3+2𝑥2+10𝑥−4 is the one that has a remainder of -43 when divided by x + 3.