Question

check whether the first polynomial is a factor of the second polynomial by applying elucids division algorithm x^2-5x+6, 10x^4+8x^2+6x+3

Answer 1

According to division algorithmDividen= Divisor × Quotient + Remainderp(x) = g(x) × q(x) + r(x),plug the value in formula we getx³ – 3x² + x + 2 = g(x)*(x-2) - 2x + 4Add 2x and subtract 4 both side we getx³ – 3x² + x + 2 + 2x – 4 = g(x) *(x-2)simplify and divide by x/2we get(x³ – 3x² + 3x– 2)/(x-2) = g(x)