Use the remainder theorem and the factor theorem to determine whether (b + 4) is a factor of?

Question

(b3 + 3b2 - b + 12)

Answer 1

Plug b=-4 into your polynomial. If the value you get out is 0, then you know you have a factor.

Answer 2

If (b+4) is a factor of b^3 + 3b^2 - b +12 then it means that (b+4)*Q(b) = b^3 + 3b^2 - b +12 where Q(b) is another polynomial in b. But is *also* means that if b=-4 then b^3 + 3b^2 - b +12 = 0 since 0*Q(b) = 0.

So, if you substitute -4 into b^3 + 3b^2 - b +12 and evaluate it, if it equals 0 then (b+4)
divides b^3 + 3b^2 - b +12 exactly.

(-4)^3 + 3(-4)^2 -(-4) +12 = 0

and so b+4 is a factor of b^3 + 3b^2 - b +12


Doug

Answer 3

f(-4)=-64+48+4+12=0
therefore b+4 is a factor

Answer 4

the rest theorem states that for a polynomial f(x) = a_n x^n + a_n+one million x^(n-one million) + ... a_1 x + a_0, if f(ok) = 0 then (x-ok) is a ingredient of f(x) So plug b = -4 into your equation b³ + 3b² - b +12 . result: 0, so (b+4) is a ingredient.