Question
Factor completely.
3u2+10u+7
3u2+10u+7
Answers
Answered by
GPT-4o mini
To factor the quadratic expression \(3u^2 + 10u + 7\), we can use the method of factoring by grouping or the AC method.
1. **Multiply the leading coefficient (3) by the constant term (7)**:
\[ 3 \times 7 = 21 \]
2. **We need to find two numbers that multiply to 21 and add to the middle coefficient (10)**:
The numbers that fit this requirement are 3 and 7 since:
\[ 3 \times 7 = 21 \quad \text{and} \quad 3 + 7 = 10 \]
3. **Rewrite the middle term (10u) using the two numbers**:
\[ 3u^2 + 3u + 7u + 7 \]
4. **Group the terms**:
\[ (3u^2 + 3u) + (7u + 7) \]
5. **Factor out the common factors from each group**:
\[ 3u(u + 1) + 7(u + 1) \]
6. **Now factor out the common binomial factor**:
\[ (3u + 7)(u + 1) \]
Thus, the expression \(3u^2 + 10u + 7\) factors completely as:
\[
\boxed{(3u + 7)(u + 1)}
\]
1. **Multiply the leading coefficient (3) by the constant term (7)**:
\[ 3 \times 7 = 21 \]
2. **We need to find two numbers that multiply to 21 and add to the middle coefficient (10)**:
The numbers that fit this requirement are 3 and 7 since:
\[ 3 \times 7 = 21 \quad \text{and} \quad 3 + 7 = 10 \]
3. **Rewrite the middle term (10u) using the two numbers**:
\[ 3u^2 + 3u + 7u + 7 \]
4. **Group the terms**:
\[ (3u^2 + 3u) + (7u + 7) \]
5. **Factor out the common factors from each group**:
\[ 3u(u + 1) + 7(u + 1) \]
6. **Now factor out the common binomial factor**:
\[ (3u + 7)(u + 1) \]
Thus, the expression \(3u^2 + 10u + 7\) factors completely as:
\[
\boxed{(3u + 7)(u + 1)}
\]
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