Question
Upstudy AI Solution
Tutor-Verified Answer
Answer
The factored form of
is
.
Solution
To factor the quadratic expression
, follow these steps:
-
Factor Out the Greatest Common Factor (GCF):First, observe that each term in the expression shares a common factor of 6.
-
Factor the Quadratic Inside the Parentheses:Now, focus on factoring the quadratic expression
. -
Find two numbers that multiply to
and add to : These numbers areand because: -
Write the Factored Form:
-
-
Combine the Factored Parts:Substitute the factored quadratic back into the expression:
Final Factored Form:
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Extra Insights
To solve the expression
, you can factor out the common term, which is 6. This simplifies the equation to
. Next, you can factor
further into
. So, the complete factored form is
.
Now you have a clear way to solve for
, making it easier to find the values where the expression equals zero. If you set
, you can quickly determine that
and
are the roots of the equation. Happy factoring!