Question

What is the factorization of the polynomial?

2x^2+28x+98

Answer 1

To factor the polynomial \( 2x^2 + 28x + 98 \), we can start by factoring out the greatest common factor (GCF).

1. **Identify the GCF**: The GCF of the coefficients \(2\), \(28\), and \(98\) is \(2\).

2. **Factor out the GCF**:
\[
2x^2 + 28x + 98 = 2(x^2 + 14x + 49)
\]

3. **Factor the quadratic** \(x^2 + 14x + 49\):
- To factor this quadratic, we look for two numbers that multiply to \(49\) (the constant term) and add to \(14\) (the coefficient of \(x\)).
- The numbers \(7\) and \(7\) satisfy these conditions.

4. **Write the quadratic in factored form**:
\[
x^2 + 14x + 49 = (x + 7)(x + 7) = (x + 7)^2
\]

5. **Combine everything**:
\[
2(x^2 + 14x + 49) = 2((x + 7)^2) = 2(x + 7)^2
\]

Thus, the complete factorization of the polynomial \( 2x^2 + 28x + 98 \) is:
\[
\boxed{2(x + 7)^2}
\]