Given:
[tex]f(x)=2x^3+12x^2-26x-84[/tex]
To find the binomial that is a factor of the polynomial:
By factor theorem,
If f(a) = 0, then the binomial (x - a) is a factor of polynomial f(x).
So, let us check the options one by one.
A) Put x = -7 in the given polynomial.
[tex]\begin{gathered} f(-7)=2(-7)^3+12(-7)^2-26(-7)-84 \\ =2(-343)+12(49)+182-84 \\ =0 \end{gathered}[/tex]
Since, f(-7)=0
Therefore, (x+7) is a factor.
Thus, the correct option is A.
