Question

show that 2x-3 is a factor of x+2x3-9x2+12​

Answer 1

Step-by-step explanation:

p(x) = x + 2x³ - 9x² + 12

g(x) = 2x - 3

2x - 3 = 0

x = 3/2

put x in p(x)

p(3/2) = x + 2x³ - 9x² + 12

= 3/2 + 2(3/2)³ - 9(3/2)² + 12

= 3/2 + 2(27/8) - 9(9/4) + 12

= 3/2 + 27/4 - 81/4 + 12

= (6 + 27 - 81 + 48)/4

= ( 81 - 81)/4

= 0/4

p(3/2) = 0

so, g(x) is a factor of p(x)

2x-3 is a factor of x + 2x³ - 9x² + 12