Question

How do you factor the expression `2x^2 + 5x - 18`?

Answer 1

`(x+9/2)*(x-2)`

Explanation:

first make sure the coefficient of `x^2` is 1
you can factorize a quadratic polynomial in the form:
`x^2+`(sum of two numbers)`x+`(product of two numbers)
let the two numbers be `a,b`
so, from the equation, we have
`a+b = 5/2` `&` `a*b = -18/2 = -9`

solve this 2 equation 2 unknown by substituting either `a=-9/b` or `b=-9/a` into the eq `a+b=5/2`
on solving you get the two numbers `a` & `b` as `9/2,-2`
now, you can write:
`x^2+(-2+9/2)x+(-2*9/2)`
`x^2-2x+9/2x-9`
`x(x-2)+9/2(x-2)`
`(x-2)*(x+9/2)`