Question
Upstudy AI Solution
Tutor-Verified Answer
Answer
The quadratic expression
Solution
It looks like you want to factor completely the quadratic expression:
Let’s factor this step by step.
Step 1: Identify the Coefficients
The quadratic is in the form:
Where:
Step 2: Multiply
Multiply the coefficients of
Step 3: Find Two Numbers That Multiply to
We need two numbers that:
- Multiply to 75
- Add up to -20
The numbers are -5 and -15 because:
Step 4: Rewrite the Middle Term Using These Numbers
Rewrite the quadratic expression by splitting the middle term:
Step 5: Factor by Grouping
Group the terms into two pairs:
Factor out the greatest common factor (GCF) from each group:
Step 6: Factor Out the Common Binomial Factor
Both groups contain the common factor
Final Factored Form
Therefore, the completely factored form of the quadratic expression is:
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Mind Expander
To factor the quadratic expression
Rewriting the expression, we have:
Next, we group and factor by parts:
This gives us:
The complete factorization is:
Now we have it all ready for any further explorations!
In the world of quadratic expressions, factoring not only simplifies solving equations but can also unveil different graph characteristics! Each factor can indicate the x-intercepts of a corresponding parabola. So, once you’ve factored it, you can easily sketch the graph for further insights, all while uncovering the beauty of mathematics.
Have you ever felt lost in quadratic equations? No worries! A common mistake is failing to recognize when to apply the quadratic formula. Before resorting to that, always check if the expression can be factored easily. It saves you time and helps you develop a keener intuition for numbers! Start by looking for a common factor or testing if the expression can be easily grouped first. Happy factoring!
