Suppose you divide a polynomial by a binomial. How do you know if the binomial is a factor of the polynomial? Create a sample problem that has a binomial which IS a factor of the polynomial being divided, and another problem that has a binomial which is NOT a factor of the polynomial being divided.

HELPP

Question

Suppose you divide a polynomial by a binomial. How do you know if the binomial is a factor of the polynomial? Create a sample problem that has a binomial which IS a factor of the polynomial being divided, and another problem that has a binomial which is NOT a factor of the polynomial being divided.

HELPP

campbell_st · Answer

ok... if the binomial is (x + a) and you have a polynomial P(x) 

then if P(-a) = 0 then (x + a) is a factor

this is known as the Factor Theorem

anonymous · Answer

What about it with numbers?

campbell_st · Answer

ok... here is a simple example 

is (x + 1) a factor of P(x) = x^2 + 3x + 2

so substitute x = -1

P(-1) = (-1)^2 + 3(-1) + 2

        =0 

so that proves (x + 1) is a factor.

anonymous · Answer

so to prove one which is not a factor what would I have to do then?

campbell_st · Answer

ok... so is (x + 3) a factor of P(x) = x^2 + 3x + 2

P(-3) = (-3)^2 + 3(-3) + 2

P(-3) = 2

since P(x) doesn't equal zero , (x +3) is not a factor.

anonymous · Answer

Oh okay! Now I see. You made that a lot more simple than my teacher explained. Thank you very much!