Question

Factor: 9x^2 + 30 + 25 A) (3x + 5)^2 B) (3x - 5)^2 C) (3x + 5)(3x - 5) D) (9x + 25)

Answer 1

To factor the expression 9x^2 + 30 + 25, first, simplify it by combining the constants:

9x^2 + 30 + 25 = 9x^2 + 55

Now, let's factor this expression further:

9x^2 + 55 can be factored as follows:

9x^2 + 55 = 9x^2 + 9 * 5 + 9 * 6

Now, factor out the common factor of 9:

9(x^2 + 5 + 6)

Now, let's factor the quadratic expression inside the parentheses:

x^2 + 5x + 6

This quadratic expression can be factored as follows:

x^2 + 5x + 6 = (x + 2)(x + 3)

So, the factored form of 9x^2 + 30 + 25 is:

9(x + 2)(x + 3)

Therefore, the correct answer is C) (3x + 2)(3x + 3).

Explanation: