Question

How do you factor 2x^2-9x-5?

Answer 1

Hello from MrBillDoesMath!

Answer:  (2x + 1) (x-5)

Discussion:

To factor the polynomial let's find its roots using the quadratic formula:

x = ( -b -+\- sqrt ( b^2 - 4ac)) / 2a which in our case is:

x =    ( - (-9) +\- sqrt ( (-9^2 - 4*2*(-5)) )   /(2*2)

x =  ( 9 +\-  sqrt (81 + 40))/4 =>

x = ( 9  +\- sqrt(121))  / 4 =>

x = ( 9 +\- 11) /4 as sqrt (121) =11

Finally then,

x = ( 9 - 11) /4  = -2/4 = -1/2 and

x = (9 + 11)/4 = 20/4 = 5

So the polynomial factors as follows:

( 2x - (-1) ) ( x - 5) or

(2x + 1) (x-5)

Thank you,

MrB