Factor the trinomial below. Write each factor as a polynomial in descending order. Enter exponents using the caret ( ^ ). For example, you would enter x2 as x^2. 25x2 + 30x + 9
(5x+3)^2 = (5x+3)(5x+3).
To factor the trinomial 25x^2 + 30x + 9, we can use the fact that it is in the form ax^2 + bx + c.
First, we find the factors of the coefficient of x^2, which is 25. The factors are 1 and 25, as well as -1 and -25. Next, we find the factors of the constant term, which is 9. The factors are 1 and 9, as well as -1 and -9.
Now, we need to find a combination of these factors that will sum up to the coefficient of x, which is 30. Looking at the factors, we notice that 25 and 9 have a sum of 34, while 1 and 25 have a sum of 26. Neither of these sums match the coefficient of x.
Since there isn't a combination of factors that add up to the coefficient of x, we can conclude that the trinomial 25x^2 + 30x + 9 is prime and cannot be factored further.
Therefore, the factored form of the trinomial is simply 25x^2 + 30x + 9.