Question

How do you factor `y= x^2-x-20` ?

Answer 1

y = (x + 4)( x- 5)

Explanation:

Find 2 numbers knowing sum (-1) and product (-20). It is the factor pairs (4, - 5). The 2 numbers are 4 and -5
y = (x + 4)(x - 5)

Answer 2

Find its solutions and write it as:

`ax^2+bx+c=a(x-x_1)(x-x_2)`

Answer is:

`x^2-x-20=(x-5)(x+4)`

Explanation:

If you find all it's solutions `(x_1,x_2,x_3...)` you can write it as a product of its solutions. If the polynomial has two solutions `(x_1,x_2)` you can solve it like this:

`ax^2+bx+c=a(x-x_1)(x-x_2)`

For `y=x^2-x-20` the two solutions:

`y=0`

`x^2-x-20=0`

`a=1`
`b=-1`
`c=-20`

`Δ=(-1)^2-4*1*(-20)=81`

`x_(1,2)=(-b+-sqrt(Δ))/(2a)=(-(-1)+-sqrt(81))/(2*1)=(1+-9)/2`

`x_1=5`

`x_2=-4`

Therefore the equation can be written:

`x^2-x-20=a(x-x_1)(x-x_2)=(x-5)(x+4)`