Find the representation of the product of the following function
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Find the representation of the product of the following function
To solve the problem of factoring the quadratic expression , we will follow these steps:
Let's proceed with these steps:
Step 1: List all pairs of integers that multiply to 32:
1 and 32
2 and 16
4 and 8
Step 2: Determine which pair of these adds up to 12:
Checking each:
The pair 4 and 8 adds up to 12.
Step 3: Use this pair to factor the quadratic expression:
Thus, .
Therefore, the factored form of is .
Create an algebraic expression based on the following parameters:
\( a=3,b=0,c=-3 \)
Start with pairs closest to the square root of the constant term. For 32, try 4 and 8 first since they're closest to √32 ≈ 5.7. This often saves time!
Then the quadratic cannot be factored using integers. You might need to use the quadratic formula or complete the square instead. Not all quadratics factor nicely!
Because both the middle term (+12x) and constant term (+32) are positive. When both are positive, both factors must be positive to give the correct signs.
Use FOIL to multiply your factors back out: . It should match the original!
That's perfectly fine! Multiplication is commutative, so . Both orders are correct answers.
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