factoring polynomial by subtraction

Question

(x^2+3x-7)-(2x^2-5x+3)

Answer 1

Given polynomial is (x^2+3x-7)-(2x^2-5x+3)

= x^2-2x^2+3x+5x-7-3

= -x^2+8x-10

= x^2-8x+10

Compare it qudratic form is ax^2+bx+c

a = 1, b = -8, c = 10

Roots are x = -b±√b^2-4ac

x = 8±√(64-4*1*10)/2*1

x = [8±√24]/2

x = [8±√4*6]/2

x = [8± 2√3]/2

x = 2[4±√3]/2

x = 4±√3

x = 4+√3   and x = 4-√3

Factoring of given polynomial is [x-(4+√3)][x-(4-√3)]