Question

find k so that x^3-2x^2+3x+k has (x-1) as a factor

Answer 1

Answer:

Assuming a typo in the equation...

Should it be 6x^3-kx^2-5x+6 ?

divide (x-3) into this polynomial and you get 6x^2+(18-k)x+[3(18-k)-5] with remainder of

3[3(18-k)-5]+6 which must equal 0

3[3(18-k)-5]+6=0

3[54-3k-5]+6=0

3[49-3k]+6=0

3[49-3k]=-6

49-3k=-2

49+2=3k

51=3k

k=51/3=17

or more simply, use Mark M.'s method: f(3) must equal 0 so replace each x with 3 to get the value of k