( 5x^4 +16x 3- x^2 -10x +6) / (x +3 )

Question

Synthetic division

Answer 1

Assume initially that x+3 is a factor of the numerator polynomial. Use zero -3 to divide by using synthetic division:

-3 | 5..16 -1 -10..6

......5 -15 -3..12 -6

......5....1 -4....2 | 0

Yes, it is a factor so the quotient is: 5x^3+x^2-4x+2. Note that this is true only if x not equal to -3, because this would create division by zero, which is disallowed.