Question

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Prove that (x - 2), (x + 3) and (x-4) are factors of the polynomial : p(x) =
x cube minus 3 x square - 10 X + 24 ​

Answer 1

Answer:

p(x)=x³-3x²-10x+24

put the (x-2)=0

p(x)=2

p(2)=(2)³-3×(2)²-10×2+24

=8-12-20+24

=32-22

=10

So, x-2 is not factors of p(x)

put (x+3)=0

x= -3

p(-3)=(-3)³-3×(-3)²-10×(-3)+24

= -27-27+30+24

= 54-54

= 0

So, x+3 is factors of p(x)

put (x-4)=0

x=4

p(4)=(4)³-3×(4)²-10×4+24

=64-48-40+24

=88-88

=0

So, x-4 is factors of p(x)

Hence, (x-3) and (x-4) is a factors of p(x)=x³-3x²-10x+24