FACTORING: !!!!!!!!!!!!!!!!!!!!!

Question

314x^3+1256x^2-7536

Answer 1

The given expression 314x³+1256x²- 7536

Take out common factor

314(x³+ 4x²- 24)

Apply synthetic division

x = 2 |  1    4     0   -24

            0   2    12   24

         ________________

            1   6    12    0

(x - 2) ( x²+ 6x+12)

Consider the quadratic equation x²+ 6x+12

Apply quadratic formula - b±√b²-4ac/2a

x =[ -6 ±√(6)²-4(1)(12)]/2(1)

x =[ -6 ±√36 -48]/2

x =[ - 6 ±√ -12]/2

x = (-6 ± 2i√3)/2

x = -3 ±i√3

The complete factorization form of expression is 314(x - 3+i√3)(x -3 -i√3)

Comments

The complete factorization form of expression is 314(x - 2)(x - 3 + i√3)(x -3 -i√3)