43. The trinomial $$ x^{2}-x-6 $$ can be factored as the product of 2 linear factors, in the form $$ (x+a)(x+b) $$. What is the polynomial sum of these 2 factors? A. $$ 2 x-1 $$ B. $$ 2 x+1 $$ C. $$ 2 x-5 $$ D. $$ 2 x+5 $$ E. $$ 2 x-6 $$

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Factor the trinomial by finding two numbers that multiply to $$-6$$ (the constant term) and add to $$-1$$ (the coefficient of $$ x $$).

1. We need numbers $$ a $$ and $$ b $$ such that:
   $$
   a \times b = -6 \quad \text{and} \quad a + b = -1.
   $$

2. The numbers $$ -3 $$ and $$ 2 $$ satisfy these conditions because:
   $$
   (-3)(2) = -6 \quad \text{and} \quad -3 + 2 = -1.
   $$

3. Thus, the trinomial factors as:
   $$
   x^2 - x - 6 = (x - 3)(x + 2).
   $$

4. The problem asks for the polynomial sum of the two factors:
   $$
   (x - 3) + (x + 2) = 2x - 1.
   $$

Therefore, the answer is $$\boxed{2x - 1}$$.
The polynomial sum of the two factors is $$ 2x - 1 $$.

The trinomial can be factored as the product
of 2 linear factors, in the form . What is
the polynomial sum of these 2 factors?
A.
B.
C.
D.
E.

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The trinomial can be factored as the product of 2 linear factors, in the form . What is the polynomial sum of these 2 factors? A. B. C. D. E.