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,

$f(4)=0$

$16a-80=0$

$16a=80$

$a=\dfrac{80}{16}$

$a=5$

Therefore, the value of a is 5.