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. The GCF is probably 5.
I did this already.
Let's start with Part 1.
To factor each binomial by finding the greatest common factor (GCF), you need to identify the largest common factor of all the terms in each binomial. In this case, the GCF for A=(x^2+5x) is x, and the GCF for B=(6x+30) is 6.
Now, let's find the factored form of each binomial:
A=(x^2+5x) = x(x+5)
B=(6x+30) = 6(1x+5)
Next, we add the factored binomials to make a single expression:
(x(x+5)) + (6(1x+5))
Now, let's simplify the expression:
x(x+5) + 6(1x+5) = x^2 + 5x + 6x + 30 = x^2 + 11x + 30
This is the answer for Part 1.
Moving on to Part 2:
We need to add the original forms of A and B to make a trinomial:
(x^2+5x) + (6x+30)
Simplifying this expression, we get:
x^2 + 5x + 6x + 30 = x^2 + 11x + 30
Now, we factor the trinomial:
The factored form of x^2 + 11x + 30 is (x+6)(x+5)
This is the answer for Part 2.
For Part 3:
In Part A, we factored the binomials A=(x^2+5x) and B=(6x+30) separately. Then we added the factored binomials to make a single expression.
In Part B, we directly added the original forms of A and B to make a trinomial, and then factored the resulting trinomial.
If you compare the factored forms from Part A and Part B, you will notice that they are the same: (x+6)(x+5).
So, to go from the answer in Part A to the answer in Part B, you could simply expand the factored form in Part A to get the original form, which is x^2 + 11x + 30.
I hope this clarifies the process for you!