Question

Factoring trinomials and difference of squares. I need to understand the steps.

Answer 1

Factoring the term
`3x^2-75` we get
`\mathbf{3(x+5)(x-5)}`

Explanation:

We need to solve the polynomial:
`3x^2-75`

First we see that 3 is common term, so taking 3 as common

`3(x^2-25)`

We know that 25 = 5x5 = 5²

So, replacing 25 with 5²

`3(x^2-5^2)`

We know that,
`a^2-b^2=(a-b)(a+b)`

Applying this in our equation:
`x^2-5^2=(x+5)(x-5)`

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

So, factoring the term
`3x^2-75` we get
`\mathbf{3(x+5)(x-5)}`