Question
2xsquared+14x+24
Answers
GPT-4o mini
To simplify or factor the quadratic expression \(2x^2 + 14x + 24\), we can start by factoring out the greatest common factor (GCF).
1. **Find the GCF**: The GCF of the coefficients 2, 14, and 24 is 2.
2. **Factor out the GCF**:
\[
2(x^2 + 7x + 12)
\]
3. **Factor the quadratic expression \(x^2 + 7x + 12\)**. We are looking for two numbers that multiply to 12 (the constant term) and add to 7 (the coefficient of the linear term). The numbers 3 and 4 meet these criteria:
\[
x^2 + 7x + 12 = (x + 3)(x + 4)
\]
4. **Combine the factors**:
\[
2(x + 3)(x + 4)
\]
Thus, the fully factored form of \(2x^2 + 14x + 24\) is:
\[
2(x + 3)(x + 4)
\]
1. **Find the GCF**: The GCF of the coefficients 2, 14, and 24 is 2.
2. **Factor out the GCF**:
\[
2(x^2 + 7x + 12)
\]
3. **Factor the quadratic expression \(x^2 + 7x + 12\)**. We are looking for two numbers that multiply to 12 (the constant term) and add to 7 (the coefficient of the linear term). The numbers 3 and 4 meet these criteria:
\[
x^2 + 7x + 12 = (x + 3)(x + 4)
\]
4. **Combine the factors**:
\[
2(x + 3)(x + 4)
\]
Thus, the fully factored form of \(2x^2 + 14x + 24\) is:
\[
2(x + 3)(x + 4)
\]