So the questions was-->Factor the following algebraic equation and describe the process by which it is done: x²+ 3x – 10 = ?

Question

I solved the questions correctly but my teacher said I need to show it algebraically not arithmetically. & she said that I need to show how I arrived with the factors (x+5)(x-2) = ?

Answer 1

factors of 10

(10,1,2,5)

since you get 5-2 = 3...you would use 5,2

(x +5)*(x-2) = foil

x^2 +(-2x)+5x-10 =

x^2 + 3x - 10

Answer 2

Make a list of factors for both the coefficient of the x^2 term and the constant. In this case, 1 and 10. so 1X1 and then 1X10 and 2X5. Also, the fact that the constant is a negative 10, that means one of the 2 binomials
must be negative. Then you look for the combination of the sets of factors that when put together with FOIL, you get the middle term, in this case, 3x.

Answer 3

Thank you both!!