Question

if x–2 is a factor of 2x³–x²–px–2
find the value of p​

Answer 1

Step-by-step explanation:

x-2=0

x=2

p(2)=2x^3 - x^2-px-2

2×2^3 -2^2-p×2-2 = 0

2×8 - 4 -p × 2 -2 = 9

16-4-p×2-2 = 0

12 - p × 2 -2 =0

-p = -12 +2 ÷2

-p = -12

p = 12

Answer 2

$\sf \Large Solution!!$

Factor Theorem → When a polynomial f(x) is divided by x-a, the remainder = f(a). And, if remainder f(a) = 0; x-a is a factor of the polynomial f(x).

x - 2 = 0

x = 2

It is given that x - 2 is a factor of 2x³ - x² - px - 2. This means that the remainder is zero.

f(x) = 2x³ - x² - px - 2

f(2) = 2(2)³ - (2)² - p(2) - 2

0 = 16 - 4 - 2p - 2

0 = 16 - 6 - 2p

0 = 10 - 2p

2p = 10

p = 10 ÷ 2

p = 5

Verification:- Put the value of p in the polynomial and the answer should be zero as x - 2 is a factor of the polynomial given.

2x³ - x² - px - 2 = 0

2(2)³ - (2)² - (5)(2) - 2 = 0

16 - 4 - 10 - 2 = 0

16 - 16 = 0

0 = 0

LHS = RHS

Hence, verified.

The value of p is 5.