Question

1 point

14. consider the polynomial
p(x) = 2x“ – (m + 3)x – 1.
If p(x) is divisible by x-2 then m=

Answer 1

If
`p(x)` is divisible by
`x-2`, then
`m = (1)/(2)`.

Explanation:

Let
`p(x) = 2\cdot x^(2)-(m+3)\cdot x - 1`, if
`p(x)` is divisible by
`x-2`, then
`p(2) = 0`. That is:

`2\cdot 2^(2)-(m+3)\cdot (2)-1 = 0`

`8 - 2\cdot m -6 -1 = 0`

`1 -2\cdot m = 0`

`2\cdot m = 1`

`m = (1)/(2)`

If
`p(x)` is divisible by
`x-2`, then
`m = (1)/(2)`.