Question

How do you factor `2x^{2}-13x+24`?

Answer 1

`f(x) = 2x^2 - 13x + 24`
`D = b^2 - 4ac = 169 - 192 = - 23`
Since D < 0 and D is not a perfect square, this f(x) can't be factored.

Answer 2

See below

Explanation:

In this case, the trinomial `a!=1` so we can use bottom-up method

Step 1: Multiply "a" to "c" (`a=2 , b=24`)
`x^2-13x+(24xx2`)
`x^2-13x+48`

Step 2: Now we can factor by using "magic X" which finds 2 numbers that can multiply equal 48 and add up to `-13`
`(x-16)(x+3)`

Step 3: Divide the numbers by the leading coefficient (`2`)
`(x-16/2)(x+3/2)`

Step 4: If the numbers divide “evenly” then this is the factor. If the numbers canNOT divide evenly, then pull the divisor up to be the leading coefficient of the x term
`(x-8)(2x+3)`
If you want to find x value, you can use Zero Product Property (set each factor equal to zero)

`x-8=0`, `x=8`
`2x+3=0`, `2x=-3`, `x=-3/2`