Question

Use the factor theorem to prove each of the following.
a. x - 3 is a factor of x3 - 9x - 9
b. x + 2 is a factor of x3 + 4x2 + 5x + 2

Answer 1

Using the factor theorem

if (x - a) is a factor then f(a) = 0

so you need to find

f(3) if f(x) = x^3 - 9x - 9 if f(3) = 0 then (x - 3) is a factor

same process for b find f(-2) if f(-2) = 0 the (x + 2) is a factor

hope it helps

Answer 2

how does this prove it though? just by showing f(3) if f(x) = x3 - 9x - 9 then stating (x - 3)? do i need to show more than that?

Answer 3

can someone just give me the answer and that way i can find out how it's done?

Answer 4

if there is a remainder... for f(a) then a can't be a factor...

for for f(3) you have f(3) = 3^3 - 9(3) - 9

if f(3) = 0 then (x - 3) is a factor... if not its not a factor... simple as that...

you could prove it by polynomial division or synthetic division but this is the simplest way

Answer 5

here is the polynomial division version



the remainder is the same as finding f(3)