Question

or
Factor completely.
7w2+9w+2

Answer 1

To factor the quadratic expression \( 7w^2 + 9w + 2 \) completely, we can use the method of factoring by grouping or the quadratic formula to find its roots.

1. **Find two numbers that multiply to \( a \cdot c \) and add to \( b \):**
- Here, \( a = 7 \), \( b = 9 \), and \( c = 2 \).
- We need two numbers that multiply to \( 7 \cdot 2 = 14 \) and add to \( 9 \).
- The numbers that meet these criteria are \( 7 \) and \( 2 \) (since \( 7 \cdot 2 = 14 \) and \( 7 + 2 = 9 \)).

2. **Rewrite the middle term using the two numbers:**
\[
7w^2 + 7w + 2w + 2
\]

3. **Group the terms:**
\[
(7w^2 + 7w) + (2w + 2)
\]

4. **Factor out common factors in each group:**
\[
7w(w + 1) + 2(w + 1)
\]

5. **Factor out the common binomial factor:**
\[
(7w + 2)(w + 1)
\]

Thus, the completely factored form of \( 7w^2 + 9w + 2 \) is:
\[
(7w + 2)(w + 1)
\]