Is 25x squared + 40x +15 a perfect square? And how do you factor it if it is?
25x^2 + 40x + 15 = (25x+15)(x+1)
To determine whether the expression 25x^2 + 40x + 15 is a perfect square, we can check if the quadratic trinomial can be factored into the square of a binomial.
First, let's look at the expression. The quadratic term is 25x^2, so if it is a perfect square, the square root of the coefficient of x^2 (25) should appear as part of the factored form. In this case, the square root of 25 is 5.
Next, we examine the linear term, which is 40x. To find a binomial that satisfies the perfect square pattern, we take half of the coefficient of x (40) which gives us 20. Therefore, we need to look for two numbers whose product is 20 and whose sum is 40.
After analyzing the constant term, which is 15, it is important to verify if it matches the square of the number we found earlier (5^2 = 25). In this case, 15 is not equal to 25.
Since the constant term does not match the square of the number found in the square root of the quadratic term, 25x^2 + 40x + 15 is not a perfect square.
To factor the trinomial, we can use the general factoring method for quadratic expressions of the form ax^2 + bx + c, where a, b, and c are coefficients. In this case, we can factor 25x^2 + 40x + 15 as follows:
25x^2 + 40x + 15 = (5x + 3)(5x + 5)
So, the factored form of 25x^2 + 40x + 15 is (5x + 3)(5x + 5).