Question

$find \: the \: value \: of \\ \: a \: for \: which \: (x + 1) \: is \: a \: factor \\ \: of \: (2 {x}^{3} - 3 {x}^{2} - 18x + a) \\ \\ the \: answer \: is \: a = 2$
​

Answer 1

given the quadratic equation

p(x) = 2x³ - 3x² - 18x + a

given that x + 1 is the factor of p(x)

so,

x + 1 = 0

x = -1

now,

p(-1) = 0 [-1 is zero of p(x) ]

2(-1)³ - 3(-1)² - 18(-1) + a = 0

-2 - 3 + 18 + a = 0

-5 + 18 + a = 0

13 + a = 0

a = -13

hope it helps