Answer:
f = ± 6 , g = ± 30
Step-by-step explanation:
Expand the left side using FOIL , then compare the coefficients of the terms with those on the right side.
(4x + f)(x + f)
= 4x² + 5fx + f²
compare with 4x² + gx + 36
Then constant term is
f² = 36 ( take square root of both sides )
[tex]\sqrt{f^2}[/tex] = ± [tex]\sqrt{36}[/tex]
f = ± 6
and coefficients of x- terms
g = 5f
f = - 6 ⇒ g = 5 × - 6 = - 30
f = 6 ⇒ g = 5 × 6 = 30
Thus g = ± 30
