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

Answer:

$c=2$

Step-by-step 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