Question

The coefficient of x² in the polynomial x³-6x²+12x-8 
pls say the answer fast​

Answer 1

Answer:

the cofficient of X2 in the polynomial

Answer 2

Answer:ven that p(x) = x³ - 6x² + 12x - 8

So p(2) = (2)³ - 6.(2)² + 12.2 - 8 = 8 - 24 + 24 - 8 = 0

Therefore (x-2) is a factor of p(x)

Now p(x) = x³ - 6x² + 12x - 8

p(x) = x²(x-2) - 4x² + 12x - 8

p(x) = x²(x-2) -4x(x-2) + 4x - 8

p(x) = x²(x-2) -4x(x-2) + 4(x-2)

p(x) = (x-2) (x²-4x+4)

p(x) = (x-2) (x²-2x-2x+4)

p(x) = (x-2) [x(x-2)-2(x-2)]

p(x) = (x-2) (x-2) (x-2)

Another method : By using (x-y)³ = x³ - 3x²y + 3xy² - y³

x³ - 6x² + 12x - 8

= (x)³ - 3.(x)².2 + 3.x.(2)² - (2)³

= (x-2)³

Step-by-step explanation:

Given that p(x) = x

So p(2) = (2)³ - 6.(2)² + 12.2 - 8 = 8 - 24 + 24 - 8 = 0

Therefore (x-2) is a factor of p(x)

Now p(x) = x³ - 6x² + 12x - 8

p(x) = x²(x-2) - 4x² + 12x - 8

p(x) = x²(x-2) -4x(x-2) + 4x - 8

p(x) = x²(x-2) -4x(x-2) + 4(x-2)

p(x) = (x-2) (x²-4x+4)

p(x) = (x-2) (x²-2x-2x+4)

p(x) = (x-2) [x(x-2)-2(x-2)]

p(x) = (x-2) (x-2) (x-2)

Another method : By using (x-y)³ = x³ - 3x²y + 3xy² - y³

x³ - 6x² + 12x - 8

= (x)³ - 3.(x)².2 + 3.x.(2)² - (2)³

= (x-2)³

= (x-2