Question

What is the value of b ?

Answer 1

Two polynomials are equal if the coefficients are equal.

`x^3+(3+b)x^2+(3b-2)x-6\\\downarrow\qquad\ \ \downarrow\qquad\qquad\ \ \ \ \downarrow\\x^3\ +\ \ 6x^2\ \ \ \ +\ \ \ \ \ 7x\ \ -\ 6\\\\x^3\to1=1\\x^2\to3+b=6\\x\to3b-2=7\\constans\to-6=-6\\\\3+b=6\ \wedge\ 3b-2=7\\\\3+b=6\ \ \ |-3\\b=3\\\\3b-2=\ \ \ \ |+2\\3b=9\ \ \ \ |:3\\b=3\\\\Answer:\ \boxed{b=3}\to\boxed{B.}`