Question

Factor the Polynomial? Please show steps. Thanks 9x^2-25

Answer 1

$a^2-b^2=(a-b)(a+b)\\\\ 9x^2-25 =(3x)^2-5^2=(3x-5)(3x+5)$

Answer 2

Fully factored, this polynomial is (3x + 5)(3x - 5).

To factor this, you can use the difference of two squares rule. In that rule, you take the square root of the first term and the square root of the second term. You then put them in two parenthesis together, one of which has an addition sign and one has a subtraction. Like this:

(Sqrt(1st) + Sqrt(2nd))(Sqrt(1st) - Sqrt(2nd)).

So we start by taking the square root of 9x^2, which is 3x. Then we take the square root of 25, which is 5. Now we place them in the parenthesis above.

(3x + 5)(3x - 5)

This is your final answer.