How to I factor the polynomial?

(5x + 3)(25x^2 - 15x + 9)

Step-by-step explanation:

This is a "sum of two cubes" We just memorize how to factor a sum of cubes (and a difference of two cubes) Someone else discovered it, we just have to recognize it and use a pattern to factor.

First, 125 is a perfect cube. It is 5^3. Also, 27 is 3^3. Obviously, x^3 is a cube. So the given problem could be (5x)^3 + 3^3

It will factor into a binomial (5x + 3) and a trinomial (5x)^2 - (5x)(3) + 3^2

You can see the binomial is the same as the problem but without the exponents. The other factor, the trinomial has the first term, the 5x but squared. The second term of the trinomial is the two terms of the problem, multiplied together and without any exponents, 5x•3, so 15x. The last term of the trinomial is the second term of the binomial, 3, but squared, so 3^2, thats 9. Theres a memory tool called SOAP that can help you memorize the adding and subtracting in the factors. SOAP stands for Same, Opposite, Always Positive. The 5x + 3 has that + bc the original problem has a + . Thats the Same. The trinomial has a - thats the Opposite of the original problem. The last + is always a +, so thats the Always Positive.