Factor polyomial $$ 6 g^{2}+23 g+7 $$

Question

UpStudy AI · Accepted Answer

To factor the quadratic polynomial $$ 6g^{2} + 23g + 7 $$, follow these steps:

1. **Identify the coefficients:**
   - $$ a = 6 $$
   - $$ b = 23 $$
   - $$ c = 7 $$

2. **Multiply $$ a $$ and $$ c $$:**
   $$
   a \times c = 6 \times 7 = 42
   $$

3. **Find two numbers that multiply to 42 and add up to 23:**
   - The numbers are 2 and 21, since $$ 2 \times 21 = 42 $$ and $$ 2 + 21 = 23 $$.

4. **Rewrite the middle term using these numbers:**
   $$
   6g^2 + 2g + 21g + 7
   $$

5. **Factor by grouping:**
   $$
   (6g^2 + 2g) + (21g + 7) = 2g(3g + 1) + 7(3g + 1)
   $$

6. **Factor out the common binomial:**
   $$
   (2g + 7)(3g + 1)
   $$

**Final Factored Form:**
$$
6g^{2} + 23g + 7 = (2g + 7)(3g + 1)
$$
$$ 6g^{2} + 23g + 7 = (2g + 7)(3g + 1) $$

Factor polyomial