1 MATH MC

first we need to find a
put x=3 into p(x)

p(3)
=3^3+(3^2)a+14x3+24 = 12
27+9a+42+24=12
9a=-81
a=-9

so p(x)=x^3-9x^2+14x+24

then we need to use長除法
..................x - 4
..............____________________
x^2-5x+b ) x^3-9X^2+14x +24
...................x^3-5x^2+ 4b
..................------------------------------
.........................-4x^2+(14-b)x+24
.........................-4x^2+20x -4b
........................--------------------------

since p(x) is divisible by x^2-5x+b

we have 14-b=20 and 24=-4b

the answer boths are b=-6

p(x) = x^3 + ax^2 + 14x + 24
p(3) = 3^3 + a(3)^2 + 14(3) + 24
12 = 27 +9a + 42 + 24
a = -9

Thus, p(x) = x^3 -9x^2 + 14x + 24

Let p(x) = (x + c)(x^2 - 5x + b)

By comparing the coefficient of x^2,
c - 5 = -9
c = -4

By comparing the constant term,
-4b = 24
b = -6

The answer is 'c' in the M.C.