Answer:
Step-by-step explanation:
To simplify the expression
2
�
2
+
3
�
+
7
�
2
+
�
+
10
x
2
+x+10
2x
2
+3x+7
, you'll need to perform polynomial division. Here's how you can do it:
Divide the first term of the numerator by the first term of the denominator:
2
�
2
÷
�
2
=
2
2x
2
÷x
2
=2.
Multiply the entire denominator by
2
2 and subtract it from the numerator.
Repeat the process until you cannot perform any more divisions or until the degree of the numerator is less than the degree of the denominator.
Here are the steps in detail:
2
�
+
1
−
1
�
2
+
�
+
10
2
�
2
+
3
�
+
7
−
(
2
�
2
+
2
�
+
20
)
0
�
−
13
x
2
+x+10
2x+1
2x
2
+3x+7
−(2x
2
+2x+20)
0
−1
x−13
So,
2
�
2
+
3
�
+
7
�
2
+
�
+
10
=
2
�
+
1
−
�
−
13
�
2
+
�
+
10
x
2
+x+10
2x
2
+3x+7
=2x+1−
x
2
+x+10
x−13
.
