Question
Factor completely.
3f^2 –24f+45
3f^2 –24f+45
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To factor the quadratic expression \(3f^2 - 24f + 45\), we can start by factoring out the greatest common factor (GCF) from all the terms.
The GCF of the coefficients \(3\), \(-24\), and \(45\) is \(3\).
First, factor out \(3\):
\[
3(f^2 - 8f + 15)
\]
Next, we need to factor the quadratic expression \(f^2 - 8f + 15\). We want to find two numbers that multiply to \(15\) (the constant term) and add to \(-8\) (the coefficient of the linear term).
The numbers \(-3\) and \(-5\) satisfy these conditions:
\[
-3 \cdot -5 = 15 \quad \text{and} \quad -3 + (-5) = -8
\]
Thus, we can factor the quadratic as follows:
\[
f^2 - 8f + 15 = (f - 3)(f - 5)
\]
Putting it all together, we have:
\[
3f^2 - 24f + 45 = 3(f - 3)(f - 5)
\]
So the completely factored form of \(3f^2 - 24f + 45\) is:
\[
\boxed{3(f - 3)(f - 5)}
\]
The GCF of the coefficients \(3\), \(-24\), and \(45\) is \(3\).
First, factor out \(3\):
\[
3(f^2 - 8f + 15)
\]
Next, we need to factor the quadratic expression \(f^2 - 8f + 15\). We want to find two numbers that multiply to \(15\) (the constant term) and add to \(-8\) (the coefficient of the linear term).
The numbers \(-3\) and \(-5\) satisfy these conditions:
\[
-3 \cdot -5 = 15 \quad \text{and} \quad -3 + (-5) = -8
\]
Thus, we can factor the quadratic as follows:
\[
f^2 - 8f + 15 = (f - 3)(f - 5)
\]
Putting it all together, we have:
\[
3f^2 - 24f + 45 = 3(f - 3)(f - 5)
\]
So the completely factored form of \(3f^2 - 24f + 45\) is:
\[
\boxed{3(f - 3)(f - 5)}
\]
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.