Question

If (x-2)is a factor of 2x³-x²-px-2,
then find

1:find the value of 'p'.
2:with the value of 'p', factorise the equation completely.

Answer 1

Polynomial

$= 2 {x}^{3} - {x}^{2} - px - 2$

Factor is

$p(x) = x - 2 \\ 0 = x - 2 \\ x = 2$

put value in polynomial

$0= 2 {(2)}^{3 } - {2}^{2} - p(2) - 2 \\ 0 = 2 \times 8 - 4 - 2p - 2 \\ 0 = 16 - 6 - 2p \\ 0 = 10 - 2p \\ 2p = 10 \\ p = \frac{10}{2} \\ p = 5$

here is double step verification

$0 = 16 - 6 - 2(5) \\ 0 = 10 - 10 \\ 0 = 0$

LHS = RHS

Answer 2

if (x-2)

x=2

let put x=2

2(2)³ - (2)² - px2 - 2 =0

16 - 4 - 2p -2 =0

10 - 2p =0

10 = 2p

10/2 = p

5 = p