Question

Factorize 3x^3 - 4x^2 - 12x + 16

Answer 1

Factorize 3x^3 - 4x^2 - 12x + 16

Step  1  :Equation at the end of step  1  : (((3 • (x3)) - 22x2) - 12x) - 16 = 0
Step  2  :Equation at the end of step  2  : ((3x3 - 22x2) - 12x) - 16 = 0 Step  3  :Checking for a perfect cube :

 3.1    3x3-4x2-12x-16  is not a perfect cube 

Trying to factor by pulling out :

 3.2      Factoring:  3x3-4x2-12x-16 

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  3x3-16 
Group 2:  -4x2-12x 

Pull out from each group separately :

Group 1:   (3x3-16) • (1)
Group 2:   (x+3) • (-4x)

Step  2  :Equation at the end of step  2  : ((3x3 - 22x2) - 12x) - 16 = 0 Step  3  :Checking for a perfect cube :

 3.1    3x3-4x2-12x-16  is not a perfect cube 

Trying to factor by pulling out :

 3.2      Factoring:  3x3-4x2-12x-16 

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  3x3-16 
Group 2:  -4x2-12x 

Pull out from each group separately :

Group 1:   (3x3-16) • (1)
Group 2:   (x+3) • (-4x)

Answer 2

Let p(x) = 3x3-4x2-12x+16 Put x = 2 in p(x)

p(2) = 3(2)3 – 4(2)2 – 12(2) + 16 = 3(8)– 4(4) – 24 + 16 = 0

Hence (x – 2) is a factor of p(x)

Now on dividing p(x) with (x – 2) we get the quotient as (3x2 + 2x – 8) ⇒ p(x) = (x – 2)(3x2 + 2x – 8) = (x – 2)(3x2 + 6x – 4x – 8) = (x – 2)[3x(x+2) – 4(x + 2)] = (x – 2)(x + 2)(3x – 4)