Question

Find the value of a such that (x − 4)  is a factors of 5x³ − 7x² − ax − 28.

Answer 1

Let `f(x) = 5x^3 - 7x^2 - ax - 28` be the given polynomial.

By the factor theorem,

(x − 4) is a factor of f(x).

Therefore f(4) = 0

Hence , `f(4) = 5(4)^2  - 7(4)^2 - a (4) - 28 = 0`

\[\Rightarrow 320 - 112 - 4a - 28 = 0\]

\[ \Rightarrow 180 - 4a = 0\]

\[ \Rightarrow a = \frac{180}{4} = 45\]

Hence, a = 45