Factor $$ x^{2}+5 x+6 $$ $$ (x+5)(x+1) $$ $$ (x-5)(x-1) $$ $$ (x+3)(x+2) $$ $$ (x-3)(x-2) $$

Question

UpStudy AI · Accepted Answer

We begin with the quadratic polynomial

$$
x^2 + 5x + 6.
$$

We look for two numbers $$a$$ and $$b$$ such that

$$
a + b = 5 \quad \text{and} \quad a \cdot b = 6.
$$

Considering the factors of $$6$$, we find:

$$
2 + 3 = 5 \quad \text{and} \quad 2 \times 3 = 6.
$$

Thus, the polynomial factors as

$$
(x+2)(x+3).
$$

Since multiplication is commutative, this is equivalent to

$$
(x+3)(x+2).
$$

The correct answer is $$(x+3)(x+2)$$.
The polynomial $$ x^{2}+5x+6 $$ factors to $$ (x+3)(x+2) $$.

Factor \( x^{2}+5 x+6 \) \( (x+5)(x+1) \) \( (x-5)(x-1) \) \( (x+3)(x+2) \) \( (x-3)(x-2) \)