Factoring polynomials

Question

x²+6x-48

Answer 1

We can use the quadratic formula to find the solutions of the polynomial.  Then convert them into factors.

 

x = (-b ± √(b² - 4ac)) / 2a

 

where:

a = 1

b = 6

c = -48

 

x = (-6 ± √(36 - 4(-48))) / 2

x = (-6 ± √(36 + 192)) / 2

x = (-6 ± √(228)) / 2

x = (-6 ± √4√57) / 2

x = (-6 ± 2√57) / 2

x = -3 ± √57

 

x = -3 - √57          and              x = -3 + √57

 

Then

 

x² + 6x - 48 = (x + 3 + √57)(x + 3 - √57)