Question10. Factor the following completely:
Studdy Solution
STEP 1
What is this asking?
We need to break down this expression into smaller pieces multiplied together, kind of like finding the prime factors of a number, but with *x*s!
Watch out!
Don't forget to look for **common factors** first!
It makes everything easier.
Also, double-check your answer by multiplying the factors back together.
It should match the original expression.
STEP 2
1. Find the Greatest Common Factor (GCF)
2. Factor the Trinomial
STEP 3
Let's look at our expression: .
We want to find the **biggest number** that divides evenly into **all three coefficients** (15, -27, and -6).
Think about what numbers go into all of them.
STEP 4
Looks like **3** is the greatest common factor!
So, we can **factor out** a 3 from each term: .
See how we divided each term by 3?
Now, we're left with a simpler trinomial inside the parentheses.
STEP 5
Now, we need to factor .
We're looking for two binomials that multiply together to give us this trinomial.
Since the *x* squared term has a coefficient of **5**, we know one binomial will start with and the other with .
So, we have .
STEP 6
Next, let's look at the **constant term**, which is **-2**.
We need two numbers that multiply to -2.
Our options are 1 and -2, or -1 and 2.
STEP 7
Now comes the tricky part!
We need to place these numbers in our binomials so that when we multiply everything out, the *x* term becomes **-9**.
Let's try 1 and -2. gives us .
BOOM! We found it!
STEP 8
So, the completely factored form of is .
Remember, we factored out the **3** at the beginning!
Don't leave it out of the final answer.
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