Question

1. If 2x+1 is a factor of (3b+2)x^3 + (b-1) then find b​

Answer 1

Answer:

b = 2

Step-by-step explanation:

By the Remainder Theorem, the remainder when f(x) is divided by x-a is f(a).

Since 2x+1 is a factor of (3b+2)x³ + (b-1), the remainder when (3b+2)x³ + (b-1) is divided by 2x+1 = 2( x - (-1/2) ) is 0.  So by the Remainder Theorem,

    (3b+2)(-1/2)³ + b - 1 = 0

⇒ (3b+2) / (-8) + b - 1 = 0

⇒ 3b + 2 - 8b + 8 = 0

⇒ 5b = 10

⇒ b = 2

Hope this helps!