Question

show that (2x-3)is a factor of x+2x cube - 9x square +12

Answer 1

$2x - 3 = 0 \\ x = 3 \div2 \\ substitute \: x \: in \: that \\ 3 \div 2 + 2(3 \div 2) cube - 9(3 \div 2) square + 12 = \\ 3 \div 2 + 2(27 \div 8) - 9(9 \div 4) + 12 = \\ 3 \div 2 + 27 \div 4 - 81 \div 4 + 12 = \\ 6 \div 4 + 27 \div 4 - 81 \div 4 + 12 = \\ 6 \div 4 + 27 \div 4 - 81 \div 4 + 48 \div 4 = \\ 0$