Answer:
p is -5
Explanation:
If a polynomial 2x³-9x² +15x +p is divided by (x-2), then the remainder is gotten by equating the divisor x - 2 to zero
If x - 2 = 0
Add 2 to both sides
x - 2 + 2 = 0 + 2
x = 2
Substitute x = 2 into the expression to get the remainder:
If p(x) = 2x³-9x² +15x +p
p(2)= 2(2)³-9(2)² +15(2) +p
p(2) = 2(8) - 9(4) + 30 + p
p(2) = 16-36+30+p
p(2) = -20 + 30 + p
p(2) = 10+p
Since the remainder given in question is - p, to get p, we will equate p(2) to -p as shown
p(2) = -p
10+p = -p
10 = -p-p
10 = -2p
p = 10/-2
p = -5
Hence the value of p is -5