Question

For what value of a, is the polynomial x^3 + 2x^2 - 3ax - 8 divisible by x - 4 ?​

Answer 1

Answer:

a-. 22/3

Step-by-step explanation:

Let p(x) = x3 +2x2 -3ax -8

Let p(x) = x3 +2x2 -3ax -8Given x-4 is a factor

Let p(x) = x3 +2x2 -3ax -8Given x-4 is a factorTherefore p(4) = 0

Let p(x) = x3 +2x2 -3ax -8Given x-4 is a factorTherefore p(4) = 0 43 + 2(42) – 3a(4) – 8 = 0

Let p(x) = x3 +2x2 -3ax -8Given x-4 is a factorTherefore p(4) = 0 43 + 2(42) – 3a(4) – 8 = 064 + 32 – 12a – 8 = 0

Let p(x) = x3 +2x2 -3ax -8Given x-4 is a factorTherefore p(4) = 0 43 + 2(42) – 3a(4) – 8 = 064 + 32 – 12a – 8 = 012a = 96 – 8

Let p(x) = x3 +2x2 -3ax -8Given x-4 is a factorTherefore p(4) = 0 43 + 2(42) – 3a(4) – 8 = 064 + 32 – 12a – 8 = 012a = 96 – 812a = 88

Let p(x) = x3 +2x2 -3ax -8Given x-4 is a factorTherefore p(4) = 0 43 + 2(42) – 3a(4) – 8 = 064 + 32 – 12a – 8 = 012a = 96 – 812a = 88a = 88/12 = 22/3

Let p(x) = x3 +2x2 -3ax -8Given x-4 is a factorTherefore p(4) = 0 43 + 2(42) – 3a(4) – 8 = 064 + 32 – 12a – 8 = 012a = 96 – 812a = 88a = 88/12 = 22/3a = 22/3