What is the factorization of the quadratic expression 4x² + 7x + 3?
- (x + 1)(3x + 4)
- (x + 1)(4x + 3)
- (x + 4)(x + 3)
- None of these
Explanation
To factorize 4x² + 7x + 3:
Let's find two numbers that multiply to 4*3 = 12 and add to 7:
The numbers are 4 and 3 (since 4 + 3 = 7 and 4 * 3 = 12).
Now, rewrite the middle term:
4x² + 4x + 3x + 3
Factor by grouping:
4x(x + 1) + 3(x + 1)
(4x + 3)(x + 1)
The correct answer is (x + 1)(4x + 3).
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