$$ x^{2}-x-12 $$ Factorize and solve $$ x $$

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UpStudy AI · Accepted Answer

1. We start with the quadratic polynomial:
   $$
   x^2 - x - 12
   $$

2. To factorize, we look for two numbers whose product is $$-12$$ and whose sum is $$-1$$. These two numbers are $$-4$$ and $$3$$ because:
   $$
   -4 \times 3 = -12 \quad \text{and} \quad -4 + 3 = -1
   $$

3. Thus, we can write the factorization as:
   $$
   x^2 - x - 12 = (x - 4)(x + 3)
   $$

4. To solve the equation $$x^2 - x - 12 = 0$$, we set each factor equal to zero:
   
   $$
   x - 4 = 0 \quad \text{or} \quad x + 3 = 0
   $$

5. Solving each equation:
   - From $$x - 4 = 0$$, we get:
     $$
     x = 4
     $$
   - From $$x + 3 = 0$$, we get:
     $$
     x = -3
     $$

The solutions are:
$$
x = 4 \quad \text{and} \quad x = -3
$$
$$ x = 4 $$ and $$ x = -3 $$.

Factorize and solve

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