Question

F(x)=2x^3+ax^2-37x-60

The binomial x-4 is a factor of f(x). Find the value of a.

Answer 1

Given:

The function is

`f(x)=2x^3+ax^2-37x-60`

The binomial
`x-4` is a factor of f(x).

To find:

The value of
`a`.

Solution:

If
`x-c` is a factor of f(x), then
`f(c)=0`.

It is given that,
`x-4` is a factor of f(x), then
`f(4)=0`.

We have,

`f(x)=2x^3+ax^2-37x-60`

Substituting x=4, we get

`f(4)=2(4)^3+a(4)^2-37(4)-60`

`f(4)=2(64)+a(16)-148-60`

`f(4)=128+16a-208`

`f(4)=16a-80`

Now,

`f(4)=0`

`16a-80=0`

`16a=80`

`a=(80)/(16)`

`a=5`

Therefore, the value of a is 5.