For what value of b will the polynomial P(x) = 4x^3 - 3x^2 + bx + 6 have the same remainder when it is divided by both x - 1 and x + 3?

4x^3 - 3x^2 + bx + 6 ... we can use the Remainder Theorem, here

So, if he remainders are equal, we have

4(1)^3 - 3(1)^2 + b(1) + 6 = 4(-3)^3 - 3(-3)^2 + b(-3) + 6

4 - 3 + b = -108 - 27 - 3b simplify

1 + b = -135 - 3b

136 = -4b

b = -34

thank you so much