Answer:
The factored expression is 2(x² + 5)(x + 3).
Step-by-step explanation:
Hey there!
We can use a factoring technique referred to as "grouping" to solve this problem.
Grouping is used for polynomials with four terms as a quick and easy factoring method to remove the GCF and get down to the initial terms that create the expression/function.
Grouping works in the following matter:
- Given equation: ax³ + bx² + cx + d
- Group a & b, c & d: (ax³ + bx²) + (cx + d)
- Pull GCFs and factors
Let's apply these steps to the given equation.
- Given equation: 2x³ + 6x² + 10x + 30
- Group a & b, c & d: (2x³ + 6x²) + (10x + 30)
- Pull GCFs and factors: 2x²(x + 3) + 10(x + 3)
As you'll see, we have a common term with both sides of the expression. This term, (x + 3), is a valuable asset to the factoring process. This is one of the factors for our expression.
Now, we use our GCFs to create another factor.
- List GCFs: 2x², 10
- Create a term: (2x² + 10)
Finally, we'll need to simplify this one by taking another GCF, 2.
- Pull GCF: 2(x² + 5)
Now that we have this term, we need to understand that this <em>could</em> also be factored further using imaginary numbers, but it is also acceptable to leave it in this form.
Therefore, we have our final factors: 2(x² + 5) and (x + 3).
However, when we factor, we place all of our terms together. This leaves us with the final answer: 2(x² + 5)(x + 3).
Answer:
![(2,8]](https://tex.z-dn.net/?f=%282%2C8%5D)
Step-by-step explanation:
Given
The attached piece wise function
Required
The domain
To do this, we simply consider the inequalities that bound the values of x.
The inequalities are:
and 
Combine the first two inequalities:
and
For the inequality to be true, we must have:
In interval notation, the inequality is:
Answer: 1, 2, 4, or 5
Step-by-step explanation:
The relationship in #3 is a function because all the x values are distinct, that is, none are repeated. (Y values don't matter.)
A function will not repeat any x values so if your goal is for the relationship in #4 to NOT be a function, repeat one of the x values. Any one will work.
Answer: -75
Step-by-step explanation:
45 or a random number lol just put in 45 and see if it orks
