Question

pls answer these questions

Answer 1

here is the solution. hope it helps.

Answer 2

$\bf \large \it{Hey \: User!!!}$

1. we r given that :-

p(x) = 2x³ - 6x² + 5x + k
g(x) = x - 2 = 0
x = 2

p(2) = 2(2)³ - 6(2)² + 5(2) + k = 0
>> 16 - 24 + 10 + k = 0
>> 2 + k = 0
>> k = -2

hence, the value of k = -2

2. given p(x) = 2x³ - 9x² + x + 12

g(x) = 2x - 3 = 0
2x = 3
x = 3/2

on putting values :-

p(3/2) = 2(3/2)³ - 9(3/2)² + 3/2 + 12
= 2(27/8) - 9(9/4) + 3/2 + 12
= 27/4 - 81/4 + 3/2 + 12/1
= 54/8 - 162/8 + 12/8 + 96/8
= 27/4 - 81/4 + 6/4 + 48/4
= (48-48)/4
= 0

remainder is 0 therefore (2x-3) is a factor of 2x³ - 9x² + x + 12.

$\bf \large \it{Cheers!!!}$