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
