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.

Answer 1

you should set binomial equal to 0
and then solve that for giving variable
then replace polynomial variable by that number if you get 0 then binomial is a factor of polynomial

Answer 2

for example if binomial is ( x+1)
set it equal to 0
\[\huge\rm x+1 = 0\] solve for x

Answer 3

polynomial is \[\huge\rm x^2 +4x +3\]
replace x b its value
if you get 0 then (x+1) is a factor of (x^2 +4x+3)

Answer 4

(x^2+2x+1)(x-4) how would you solve this ?

Answer 5

I'm confused on how to solve these @Nnesha

Answer 6

do you have to divide by x-4 ?

Answer 7

divide polynomial by x-4 ??***

Answer 8

I'm not sure.. we can skip that could you just help me with the example you gave me? X would equal -1 for the binomial

Answer 9

yes right now replace x by -1 in x^2 +4x +3 <--- in this polynomial
if you get 0 then x +1 is a factor of x^2 +4x +3

Answer 10

yes I did get 0

Answer 11

yes then x+1 is a factor of x^2 +4x + 3

Answer 12

\(\color{blue}{\text{Originally Posted by}}\) @ayyyyyyyyy25
(x^2+2x+1)(x-4) how would you solve this ?
\(\color{blue}{\text{End of Quote}}\)
do you have to divide or find if (x-4) is a factor of a polynomial ?

Answer 13

for (x^2+2x+1)(x-4) it says to just multiply it out @Nnesha

Answer 14

I think you divide im not sure

Answer 15

\[\huge\rm (x^2 +2x +1 )( x-4) = 0\]
or \[ \huge\rm \frac{ (x^2 +2x +1 ) }{ (x-4) }\]