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
