Answer:
p = -8
Step-by-step explanation:
Since, (x - 12) is a factor, then;
x - 12 = 0
x = 12
substitute the value of x in the equation
[tex]x^{2}[/tex] + px - 48 = 0
[tex](12)^{2}[/tex] + 12p - 48 = 0
144 + 12p -48
12p = -144 + 48
12p = -96
p = -8
So that,
[tex]x^{2}[/tex] +-8x - 48 = 0
[tex]x^{2}[/tex] -12x + 4X- 48 = 0
([tex]x^{2}[/tex] -12x) + (4X- 48)
X(X - 12) + 4(X - 12)
(X - 12) (X + 4)
Therefore, p = -8 and (X - 12) (X + 4) are factors of the equation.
