Consider the following binomials.

A=(x^2+5x) B=(6x+30)

Part 1: Factor each binomial by finding the GCF. Then, add the two factored binomials to make a single expression.

Part 2: Now add the original forms of binomial A and B together to make a trinomial. Factor the trinomial.

Part 3: Do you see something you could do to your answer in Part A to get your answer to Part B? Explain.

I know how to factor the binomials by finding the GCF. But I'm confused in this case for Parts A and B

I did this one already. How many times did you post it anyway?

In Part 1, let's find the greatest common factor (GCF) of the binomials A and B to factor them.

For A=(x^2+5x), the GCF can be found by looking at the terms' coefficients (numbers in front of the variables). In this case, the coefficients of x^2 and x are both 1. So the GCF is 1x (or simply x).

To factor A, we can take out the GCF from both terms:
A = x(x+5)

Similarly, for B=(6x+30), we can find the GCF by looking at the coefficients of x. In this case, the coefficients of 6x and 30 are both divisible by 6. So the GCF is 6.

To factor B, we can take out the GCF from both terms:
B = 6(x+5)

Now, to create a single expression by adding the two factored binomials, we add A and B together:
A + B = x(x+5) + 6(x+5)

In Part 2, we need to add the original forms of binomial A and B to make a trinomial. So let's add the original forms together:
A + B = (x^2+5x) + (6x+30)

This gives us:
A + B = x^2 + 5x + 6x + 30

Simplifying further, we have:
A + B = x^2 + 11x + 30

In Part 3, if we compare the result we got in Part 2 with the original expression in Part 1, we can see that both expressions are the same:
A + B = x^2 + 11x + 30
A + B = (x+5)(x+6)

Here, we can notice that the factored form of the trinomial obtained in Part 2 is the same as the sum of the factored binomials from Part 1.

Therefore, we can say that factoring the original expressions by finding the GCF and adding them together gives us the same result as factoring the trinomial directly.