Answer: (x-2)(2x+5)
For a polynomial of the form a x 2 + b x + c
rewrite the middle term as a sum of two terms whose product is a x (times) c = 2 − 10 = − 20 and whose sum is b = 1
2 x 2 − 4 x + 5 x − 10 = 0
2 x ( x − 2 ) + 5 ( x − 2 ) = 0
( x − 2 ) ( 2 x + 5 ) = 0
x − 2 = 0
2 x + 5 = 0
Set the first factor equal to 0
x − 2 = 0
Add 2 to both sides of the equation.
x = 2
Set the next factor equal to 0
2 x + 5 = 0
Subtract 5 from both sides of the equation.
2 x = − 5
Divide each term by 2 and simplify.
x = − 5 /2
The final solution is all the values that make = ( x − 2 ) ( 2 x + 5 ) = 0 = true.
x = 2 , − 5 / 2