Question2. Consider the exprestion .
Which expression is equivaient to ?
A
B.
C.
D.
Part B
Which expressions are factors of ?
Select all that apply.
A.
B.
C.
D.
E.
3. The function is defined as .
Part A constant. What is the value of ?
Enter your answer in the box.
Studdy Solution
STEP 1
1. We need to find an expression equivalent to .
2. We need to identify factors of the same expression.
3. We need to find the constant in the function .
STEP 2
1. Simplify and factor the expression to find the equivalent expression.
2. Identify factors of the expression.
3. Simplify the function to find the constant .
STEP 3
Factor the expression .
Notice that the expression can be grouped as follows:
Factor out the common terms in each group:
Factor by grouping:
STEP 4
Compare the factored expression with the given options:
The expression matches option D.
STEP 5
Identify factors of the expression .
From the factored form , we can see the factors are:
- , which can be further factored as
-
Thus, the factors are:
- (Option B)
- (Option C)
- (Option E)
STEP 6
Simplify the function .
First, expand both terms:
Combine like terms:
Factor out the common factor :
Factor the quadratic:
Thus, the function is:
The constant is .
The equivalent expression for Part A is option D.
The factors for Part B are options B, C, and E.
The value of for Part A of the function is .
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