How do you use the remainder theorem and the factor theorem to determine whether (b+4) is a factor of #(b^3 + 3b^2 − b + 12)#?

1 Answer
Apr 14, 2016

#(b+4)# is a factor of #b^3+3b^2-b+12#

Explanation:

Remainder theorem states that if we divide a polynomial function #f(x)# by #(x-a)#, the remainder is #f(a)#.

Hence, if #(x-a)# is a factor of #f(x)#, #f(a)=0# (This is factor theorem.)

As we have to determine whether #(b+4)# is a factor of #f(b)=b^3+3b^2-b+12# or not,

we should evaluate #f(-4)# which is equal to

#(-4)^3+3(-4)^2-(-4)+12=-64+48+4+12=0#

Hence #(b+4)# is a factor of #b^3+3b^2-b+12#.