What is the side length of a square with an area of 25x^2 -30+9 ? I'm completely confused on this problem. I do not understand how to factor using the GCF.

There is no GCF here.

I assume your -30 is supposed to be -30x. Right?

(5x-3)(5x-3)

This is a perfect square.
You can tell because 5x times 5x
equals the first term and -3 times -3 equals the 9.

When you have perfect squares in the first and last term of the trinomal try the form (ax -b)(ax-b)

I knew to use negatives because the middle term was a negative.

This can also be written as (ax-b)^2

s^2 = (5x - 3)(5x - 3) = (5x-3)^2

so
s = 5x-3

when in danger or in doubt:
http://www.mathportal.org/calculators/polynomials-solvers/polynomial-roots-calculator.php

To find the side length of a square with an area of 25x^2 - 30x + 9, you'll need to factor the quadratic expression. Factoring is the process of expressing a polynomial as the product of its factors.

Let's break down the steps to factor the quadratic expression:

Step 1: Determine if the expression can be factored. In this case, 25x^2 - 30x + 9 is a quadratic trinomial, so it can be factored.

Step 2: Look for the greatest common factor (GCF) among the terms. In this case, there is no common factor among the terms.

Step 3: Factor the quadratic trinomial. To do this, we need to find two binomials that, when multiplied, give us the original quadratic expression. The binomial factors will have the form (ax + b)(cx + d), where a, b, c, and d are constants.

In this case, we have 25x^2 - 30x + 9. To factor this expression, we need to look for two numbers that multiply to give 9 (the constant term), and add up to -30 (the coefficient of the x-term).

The two numbers that satisfy these conditions are -3 and -3. Therefore, we can factor the quadratic expression as:

(5x - 3)(5x - 3)

Step 4: Simplify the factored form. In this case, since both binomial factors are the same, we can write it as:

(5x - 3)^2

Now that the expression is factored, we can determine the side length of the square.

The side length of the square is equal to the square root of the area. Therefore, the side length is:

√(25x^2 - 30x + 9)

Simplifying this expression:

√((5x - 3)^2)

Which equals:

5x - 3

So, the side length of the square with an area of 25x^2 - 30x + 9 is 5x - 3.

To find the side length of a square with a given area, you need to take the square root of that area. However, before we can do that, we need to simplify the expression for the area.

The given expression for the area is 25x^2 - 30 + 9. To factor out the greatest common factor (GCF) from this expression, we first need to identify the common factors of all the terms.

In this case, there are no common factors (other than 1) between all the terms. So we can move on to the next step.

Next, we need to factor the expression inside the parentheses. This involves finding two numbers whose product is the constant term (9) and whose sum is the coefficient of the middle term (-30).

The constant term, 9, has only one pair of factors: 1 and 9, or -1 and -9. However, the sum of these factors is not -30.

Since there are no other pairs of factors possible, we can conclude that the expression 25x^2 - 30 + 9 is a prime polynomial, which means it cannot be factored further.

Now, we can find the side length of the square. We take the square root of the simplified expression:

√(25x^2 - 30 + 9) = √(25x^2 - 21)

Thus, the side length of the square is √(25x^2 - 21).