Express the polynomial as a product of linear factors.

Question

f(x) = 2x^3 + 4x^2 - 2x - 4

Answer 1

Just like in the last problem you asked,

 

Find the factors using synthetic division.

 

The only options are ±(4/1), ±(4/2), ±(4/4)  or  ±4, ±2, ±1

 

Try all of these and see which give you zeros for remainders.

 

Once you find one, factor the remaining quadratic.

 

Using x = -2:  you find a remainder of 0 and a reduced polynomial of 2x²-2 = 0

 

With x=-2 as a root, the factor is  (x+2)

 

With 2x²- 2=0, factor out a 2 and find 2(x²-1)  which factors into 2(x-1)(x+1)

 

And so these are your linear factors.

 

As a product:  f(x)=2(x+2)(x+1)(x-1)

Answer 2

f(x) = 2x³ +4x² - 2x - 4

f(x) = 2x²(x + 2) - 2(x + 2)

f(x) = (2x² - 2)(x + 2)

f(x) = 2(x² - 1)(x+2)

f(x) = 2(x + 1)(x - 1)(x + 2)