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