Answer:
(a) check the explanation
(b) the possible values of b is 6i or -29
Explanation:
Given function;
16x⁴ - 4x³– 4b²x² + 7bx + 18
(a)
factor of the given function = 2x + b
then, 2x + b = 0
x = -b/2
substitute the value of b into the given function;
16x⁴ - 4x³– 4b²x² + 7bx + 18
[tex]16(\frac{-b}{2} )^4 -4(\frac{-b}{2})^3-4b^2(\frac{-b}{2})^2 +7b(\frac{-b}{2})+18=0\\\\b^4+\frac{b^3}{2} -b^4-\frac{7b^2}{2} +18=0\\\\\frac{b^3}{2} -\frac{7b^2}{2} +18=0\\\\multiply\ through \ by \ "2"\\\\b^3-7b^2+36 =0 \ (shown)[/tex]
(b)
b³ - 7b² + 36 = 0
b²(b - 7) + 36 = 0
b²(b - 7) = -36
b² = -36 or b - 7 = -36
b = √(-36) or b = -36 + 7
b = √(-1) x √(36) or b = -29
b = 6i or -29
