Steps for factoring and then solving please: `(x-4)^3 -4(3x-16)=0` (x-4)^3 -4(3x-16)=0 (same thing typed)

2 Answers

durbanville's profile pic

durbanville | High School Teacher | (Level 2) Educator Emeritus

Posted on

`(x-4)^3 - 4(3x-16)=0`

Expand so that like terms can be arranged together to solve. As we have `(x-4)^3`  which may be difficult to factorize, do it in stages by doing `(x-4)^2` first:

`(x-4)(x^2 - 8x +16) - 12x + 64 = 0`

Note the changing of the symbol when multiplying the`-4 times -16=64`  

Now multiply the other `(x-4)` in:

`(x^3 - 8x^2 +16x - 4x^2+32x -64 ) - 12x +64=0`

Put like terms together and add/subract as required:

`x^3 -12x^2 +36x = 0`


`x(x^2 -12x +36) = 0`

`therefore x=0 and (x^2 -12x +36) = 0`

Factorize using the factors of the 1st and 3rd terms ie `x times x`  and the only factors that will work to render a middle term of -12 ie `(6 times 6)` :


`therefore x=6`

`therefore` x=0 and x=6

pramodpandey's profile pic

pramodpandey | College Teacher | (Level 3) Valedictorian

Posted on



Open brackets




factor out x

`x (x^2-12x+36)=0`





 This means

either x=0   or `(x-6)^2=0`



So answer