Question

What is the factorization of the polynomial below?
2x^2+ 20x+50
0 (x+2)(x+5)
02 x+ 5)(x+ 5)
0(2x+5)(x+5)
0 (x+5)(x+10)

Answer 1

To factor the polynomial \(2x^2 + 20x + 50\), we can follow these steps:

1. **Factor out the Greatest Common Factor (GCF)**:
The GCF of the coefficients \(2, 20, \) and \(50\) is \(2\). We can factor that out:
\[
2(x^2 + 10x + 25)
\]

2. **Factor the quadratic inside the parentheses**:
We now need to factor \(x^2 + 10x + 25\). This expression can be factored into:
\[
(x + 5)(x + 5) \text{ or } (x + 5)^2
\]

3. **Putting it all together**:
So the complete factorization of the original polynomial is:
\[
2(x + 5)^2
\]

Now, let's compare this with the options you provided:

- \(0 \) (x+2)(x+5)
- \(02 (x+ 5)(x+ 5)\)
- \(0(2x+5)(x+5)\)
- \(0 (x+5)(x+10)\)

The correct factorization corresponds to the option \(02 (x+ 5)(x+ 5)\), which is equivalent to \(2(x + 5)^2\).

Therefore, the factorization of the polynomial \(2x^2 + 20x + 50\) is:
\[
2(x + 5)^2
\]