Question

Choose the expressions that are equivalent to x² + 4x + 3. Select ALL that apply.

A. (x + 2)2-1
B. (x + 2)² + 1
C. (x - 1)(x - 3)
D. (x + 1)(x + 3)
E. (x - 1)(x + 4)

Answer 1

The expressions that are equivalent to x² + 4x + 3 are (A) (x + 2)² - 1, (C) (x - 1)(x - 3), and (D) (x + 1)(x + 3).

Step-by-step explanation:

The expressions that are equivalent to x² + 4x + 3 are:

1. (A) (x + 2)² - 1: This expression can be simplified to x² + 4x + 3, as expanding (x + 2)² gives x² + 4x + 4, and subtracting 1 gives x² + 4x + 3.
2. (C) (x - 1)(x - 3): Multiplying these binomials gives x² - 4x + 3, which is equivalent to x² + 4x + 3.
3. (D) (x + 1)(x + 3): Multiplying these binomials also gives x² + 4x + 3.

Therefore, options A, C, and D are equivalent expressions to x² + 4x + 3.

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