Question

How do you factor `4x^4-5x^2-9`?

Answer 1

`(2x-3)(2x+3)(x+i)(x-i)`

Explanation:

`"using the a-c method to factor"`

`"the factors of the product "4xx-9=-36`

`"which sum to - 5 are + 4 and - 9"`

`"split the middle term using these factors"`

`4x^4+4x^2-9x^2-9larrcolor(blue)"factor by grouping"`

`=4x^2(x^2+1)-9(x^2+1)`

`"take out the "color(blue)"common factor "(x^2+1)`

`=(x^2+1)(4x^2-9)`

`4x^2-9" is a "color(blue)"difference of squares"`

`"which factors in general as"`

`•color(white)(x)a^2-b^2=(a-b)(a+b)`

`4x^2=(2x)^2rArra=2x`

`9=(3)^2rArrb=3`

`4x^2-9=(2x-3)(2x+3)`

`x^2+1" can also be factored using difference of squares"`

`=(x+i)(x-i)`

`4x^4-5x^2-9=(2x-3)(2x+3)(x+i)(x-i)`