If we want to factor 2a² + 3ab + 2a + 3b + 1, the correct result is ( ).
Options
A
(2a + 3b)(a + 1)
B
(2a + 3b)(a + 1) + 1
C
a(2a + 3b) + (2a + 3b) + 1
D
(2a + 3b) + (2a + 3b) + 1
Answer & Analysis
Answer
B
Analysis
To factor the polynomial 2a² + 3ab + 2a + 3b + 1, let's follow the factor by grouping method:
Step 1: Group the terms: (2a² + 3ab) + (2a + 3b) + 1
Step 2: Factor out the common factor from each group:
In the first group, we can factor out a: a(2a + 3b).
In the second group, there is no common factor: (2a + 3b).
Now, we have: a(2a + 3b) + (
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