Question

Find the value of P for which (x+1) is a factor
of ( x ⁴+(p-3)x³-(3p-5)+x²+(3p-9)x+6.​

Answer 1

Given

Find the value of P for which (x+1) is a factor

of ( x ⁴+(p-3)x³-(3p-5)+x²+(3p-9)x+6)

To find

Find the value of p

Solution

=> x + 1 = 0

=> x = -1

Putting the value of x

=> x⁴ + (p-3)x³ - (3p-5) + x² + (3p-9)x + 6 = 0

=> (-1)⁴ + (p-3)(-1)³ - (3p-5) + (-1)²+ (3p-9)(-1) +6=0

=> 1 + (p-3)(-1) - 3p + 5 + 1 - 3p + 9 = 0

=> 1 - p + 3 - 3p + 6 - 3p + 9 = 0

=> -p - 3p - 3p + 1 + 3 + 6 + 9 = 0

=> -7p + 19 = 0

=> 19 = 7p

=> p = 19/7

Hence, the value of p is 19/7