Question

Which of the following polynomial when divided by x-6 the remainder is 0? *

x^2-4x+3
x^2-3x-18
x^2+6x-16
x^2+10x+25​

Answer 1

Aim : To find which polynomial given, results in 0, when divided by (x-6).

Option 1

p(x) = x² - 4x + 3

g(x) = x - 6

by using reminder theorem,

g(x) = x - 6 = 0

=≥ x = 0 + 6

=≥ x = 6

substituting,

p(6) = (6)² - 4(6) + 3

p(6) = 36 - 24 + 3

p(6) = 15

Reminder ≠ 0.

Hence it's not option 1

Option 2

p(x) = x² - 3x - 18

g(x) = x - 6

by using reminder theorem

g(x) = x - 6 = 0

=≥ x = 6

p(6) = (6)² - 3(6) - 18

p(6) = 36 - 18 - 18

p(6) = 36 - 36

p(6) = 0

Reminder = 0.

Therefore option 2 is correct

Option 3

p(x) = x² + 6x - 16

g(x) = x - 6

as we already know the value of x, by substituting

p(6) = (6)² + 6(6) - 16

p(6) = 36 + 36 - 16

p(6) = 56

Reminder ≠ 0.

hence it cannot be option 3.

Option 4

p(x) = x² + 10x + 25

g(x) = x - 6

by substituting the value,

p(6) = (6)² + 10(6) + 25

p(6) = 36 + 60 + 25

p(6) = 121

Reminder ≠ 0.

By the above solutions we can conclude that option 2 is correct.