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.

PLEASE HELP I DO NOT UNDERSTAND THIS

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. 

PLEASE HELP I DO NOT UNDERSTAND THIS

anonymous · Answer

can you please give me a sample problem

anonymous · Answer

@Luis_Rivera

campbell_st · Answer

just use the factor theorem 

if (x -a) if a factor ot P(x)   a polynomial then 

P(a) = 0 

so by substituting a into the polynomial you will have a zero remainder

campbell_st · Answer

so if you polynomial is 

$$P(x) = x^2 - 5x + 6 $$

to show (x -3) is  factor subsitute x = 3 into P(x) 

$$P(3) = 3^2 - 5\times 3 + 6 = 9 = 15 + 6 = 0$$

since P(3) = 0 then (x - 3) is a factor

anonymous · Answer

awesome this is great thanks

campbell_st · Answer

so for the 2nd part of the problem 

show  (x -1) isn't a factor by finding P(1) 

since its not zero... then its not a factor