Question

Solve in brief 3x square - x-4??

Answer 1

`(3x-4)(x+1)`

Explanation:

(This is a method my teacher developed; it gives the right answer but you should know the other ways to do it before start learning this method)

`3x^2-x-4 -> ax^2+bx+c`

Multiply the `c` by the coefficient of `x^2`

`x^2-x-12`

Then, find the factors that make -12 and add up to -1.

`(x-4)(x+3)`

Put the coefficient of `x^2` back into each bracket and simplify.

`(3x-4)(3x+3) -> (3x-4)(x+1)`

`3x^2-x-4 = (3x-4)(x+1)`

Answer 2

`x=4/3" or "x=-1`

Explanation:

`"to solve the quadratic equate to zero and factor"`

`rArr3x^2-x-4=0`

`"using the a-c method of factoring"`

`"the factors of the product "3xx-4=-12`

`"which sum to - 1 are + 3 and - 4"`

`"split the middle term using these factors"`

`3x^2+3x-4x-4=0larrcolor(blue)"factor by grouping"`

`color(red)(3x)(x+1)color(red)(-4)(x+1)=0`

`"take out the "color(blue)"common factor "(x+1)`

`rArr(x+1)(color(red)(3x-4))=0`

`"equate each factor to zero and solve for x"`

`x+1=0rArrx=-1`

`3x-4=0rArrx=4/3`