Question
Upstudy AI Solution
Tutor-Verified Answer
Answer
Solution
-
Recognize the quadratic polynomial:
-
Identify the pattern. Notice that the constant term
is a perfect square since and the coefficient of is twice (with a negative sign), which suggests the form: -
Factor the given quadratic using the pattern:
Thus, the factored form is:
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Mind Expander
This quadratic expression is a perfect square trinomial! You can factor it as
or simply
. This means that the value
is a double root, making it a nice example of how neat some quadratics can be when they turn out to be perfect squares.
To double-check your work, just expand
back to the original equation. You’ll find that it simplifies back to
. This is a great way to check your factoring skills!