Question

if p(x) =x³-4x²+X+6.then show that p (3) =0and hence factorise P(x) =x³-4x²+x+6..​

Answer 1

it final ans at the bottom

Answer 2

Answer:

P(x) = x³ - 4x² + x + 6

=> p (3) = ( 3)³ - 4(3)² + (3) + 6

=> p(3) = 27 - 36 + 3 + 6

=> p(3) = 27 - 36 + 9

=> p(3) = 27 + 9 - 36

=> p(3) = 36 - 36

=> p(3) = 0

Now,

x³ - 4x² + x + 6

= x³ - 2x² - 2x² + 4x - 3x + 6

= x² ( x - 2) - 2x ( x - 2) - 3(x - 2)

= ( x - 2) (x² - 2x - 3)

= (x-2) [ x² - 3x + x - 3]

= (x - 2) [ x (x - 3) + 1 (x - 3)]

= (x-2)(x-3) (x+1)