Question

what is the value of p for which the polynomial x cube minus 4 x square - 2 x minus 6 is completely divisible by x minus one

Answer 1

$\underline{ \: Hello Friend }$

Let g ( x ) = x -1

since g ( x ) = 0

then , x = 1

and also

f ( x ) = x³ + 4x² -2x - 6p = 0

f ( 1 ) = 1³ + 4 - 2 - 6p = 0

= 5 - 2 -6p = 0

= 3 - 6p = 0

$\bf { p = \frac{1}{2} }$

Hope that helps you ☺

Answer 2

Let g ( x ) = x -1

since g ( x ) = 0

then , x = 1

and also

f ( x ) = x³ + 4x² -2x - 6p = 0

f ( 1 ) = 1³ + 4 - 2 - 6p = 0

= 5 - 2 -6p = 0

= 3 - 6p = 0
= P =1/2
May I help you....
:-)
:-)