Question

The expression ( x − 12 ) is a factor of x 2 + p x − 48 . What is the value of p ?

Answer 1

p = -8

Explanation:

Since, (x - 12) is a factor, then;

x - 12 = 0

x = 12

substitute the value of x in the equation

`x^(2)` + px - 48 = 0

`(12)^(2)` + 12p - 48 = 0

144 + 12p -48

12p = -144 + 48

12p = -96

p = -8

So that,

`x^(2)` +-8x - 48 = 0

`x^(2)` -12x + 4X- 48 = 0

(
`x^(2)` -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.