the polynomial x^4-2x^3 +3x^2-ax+3a-7 when divided by x+1 leaves remainder 19 .find [a]

Question

At last it is still in variable.

Answer 1

Subtract 19: x^4-2x^3+3x^2-ax+3a-26. Because we removed the remainder, x+1 must be a factor of the revised polynomial. We can use synthetic division to divide by x+1 using -1 as the root. When we do this we end up with 4a-20. This must be equal to zero for there to be no remainder, so 4a-20=0 and a=5.

-1 | 1 -2 3 -a  (3a-26)

......1 -1 3 -6  (a + 6)

......1 -3 6 (-a-6) | 0  4a-20=0, 4a=20, a=5.

Polynomial was x^4-2x^3+3x^2-5x+8.