Question

marya wants to factor the polynomial 36x3 – 22x2 – 144x. which term can she add to the polynomial that would not change its greatest common factor? check all that apply. a. 11 b. 50xy c. 40x2 d. 24 e. 10y

Answer 1

It's Either c. 40x2 Or B.50xy

Answer 2

we have

`36x^(3) - 22x^(2) - 144x`

Step
`1`

Find the GCF of the polynomial

we know that

`36=2^(2) *3^(2) \\ Factors=1,2,3,4,6,9,12,18,36`

`x^(3)\\ Factors=1,x,x^(2),x^(3)`

`22=2*11\\ Factors=1,2,11,22`

`x^(2)\\ Factors=1,x,x^(2)`

`144=2^(4) *3^(2) \\ Factors=1,2,3,4,6,9,12,18,24,36,48,72,144`

`x\\ Factors=1,x`

So

`GCF=2x`

`36x^(3) - 22x^(2) - 144x=2x*(18x^(2) - 11x - 72)`

analyze each case

case 1)
`11`

`11=1*11\\ Factors=1,11`

the new GCF will be different
`GCF=1`

`36x^(3) - 22x^(2) - 144x+11=(1)*(36x^(3) - 22x^(2) - 144x+11)`

case 2)
`50xy`

`50=2*5^(2)\\ Factors=1,2,25,50`

`xy\\ Factors=1,x,y,xy`

the new GCF will be the same
`GCF=2x`

`36x^(3) - 22x^(2) - 144x+50xy=(2x)*(18x^(2) - 11x - 72+25y)`

case 3)
`40x^(2)`

`40=2^(3)*5\\ Factors=1,2,8,10,20,40`

`x^(2)\\ Factors=1,x,x^(2)`

the new GCF will be the same
`GCF=2x`

`36x^(3) - 22x^(2) - 144x+40x^(2)=(2x)*(18x^(2) - 11x - 72+20x)`

case 4)
`24`

`24=2^(3)*3\\ Factors=1,2,4,6,12,24`

the new GCF will be different
`GCF=2`

`36x^(3) - 22x^(2) - 144x+24=(2)*(18x^(3) - 11x^(2) - 72x+12)`

case 5)
`10y`

`10=2*5\\ Factors=1,2,5,10`

`y\\ Factors=1,y`

the new GCF will be different
`GCF=2`

`36x^(3) - 22x^(2) - 144x+10y=(2)*(18x^(3) - 11x^(2) - 72x+5y)`

therefore

the answer is

`50xy`

`40x^(2)`