Question

In the polynomial g(x) defined, c is a constant. If g(x) is divisible by x, what is the value of c? g(x) = 2(x2 + 14x + 7) − 7(x + c)

Answer 1

`c=2`

Explanation:

Step 1

The first step is to simplify expand the the equation and collect like terms. This calculation is shown below,

`g(x)=2\bigl(x^2+14x+7\bigr)-7(x+c)\\g(x)=2x^2+28x+14-7x-7c\\g(x)=2x^2+21x+14-7c\\g(x)=x(2x+21)+7(2-c).`

Step 2

The second step is to realize that that x woll divide g only if the constant term is 0.

`7(2-c)=0\\\implies 2-c=0\\\implies 2=c.`

The value of c is 2