Question

Factor completely 36x2 − 25.

Select one:
a. (6x − 5)(x + 5)
b. (6x + 5)(6x + 5)
c. (6x − 5)(6x − 5)
d. (6x + 5)(6x − 5)

Answer 1

36x^2 - 25 =
(6x - 5)(6x + 5) <===

Answer 2

Option (d) is correct.

The factored form of the given polynomial
`36x^2-25` is
`(6x+5)(6x-5)`

Explanation:

Given: Polynomial
`36x^2-25`

We have to factorize the given polynomial
`36x^2-25` completely and choose the correct option from the given options.

Consider the given polynomial
`36x^2-25`

We can rewrite the given polynomial a square of two terms,

`36x^2-25=(6x)^2-5^2`

Now, applying algebraic identity

`a^2-b^2=(a+b)(a-b)`

Thus,
`(6x)^2-5^2=(6x+5)(6x-5)`

Thus, The factored form of the given polynomial
`36x^2-25` is
`(6x+5)(6x-5)`