Question

plzzzz.do it fast.....

Answer 1

hello

x-2 is a factor of the poly.

p(2) = 2(2)3 - l(2)2 + m(2) -6 =0

p(2) = 2(8) - 4l +2m -6 =0

p(2) = 16 - 6 - 4l +2m =0

p(2) = 10 - 4l +2m

p(2) = 4l -2m = 10

p(2) = 2l -m = 5

now, x-3

p(3) = 2(3)3 - l(3)2 + m(3) -6 = 3

p(3) = 54 - 9l + 3m - 6 = 3

p(3) = 48 -9l +3m = 3

p(3) = 48 - 3 - 9l +3m= 0

p(3) = 45 -9l +3m =0

p(3) = 15 -3l + m =0

p(3) = 3l - m = 15

now,

(3l-m = 15) - (2l -m = 5)

m and m will cancel out

l = 10 and m = 15

now just verify

2(2)3 - 10(2)2 + (15)2 - 6 = 0

2(8) - 40 + 30 - 6 =0

16 - 6 -40 +30 =0

10 - 10 =0

hence proved