Question

Prove that (x-2) , (x+3) and (x-4) are the factors of polynomial

Answer 1

p(2)=8-12-20+24=0
hence, (x-2) is factor as it divides p(x)

p(-3)= -27-27+30+24=0
hence, (x+3) is a factor

p(4)= 64-48-40+24=0
hence, (x-4) is factor

Answer 2

$p(2) = {2}^{3} - 3 \times {2}^{2} - 10 \times 2 + 24 \\ \: \: \: \: \: \: \: \: \: = 8 - 12 - 10 - 24 \\ \: \: \: \: \: \: \: \: \: = 0$