✔ The numbers multiplying to 6 and adding to -5 are -2 and -3.
Q2. If (x - 4)(x + 1) = 0, what is one root?
✔ Setting the first factor to zero gives x equals 4.
Q3. Which step is crucial before solving factors?
✔ Verifying the split numbers ensures correct factorization.
Show transcript
[Slide 1] Understanding Factorization Intuition
We solve quadratic equations by breaking them into simpler parts. If the product is zero, one factor must be zero. This helps us find the roots easily.
[Slide 2] Splitting the Middle Term
First, multiply the coefficient of x squared by the constant. Find two numbers that multiply to this product and add to the middle coefficient. Split the middle term accordingly.
[Slide 3] Worked Example Step One
Let us solve the equation x squared minus five x plus six equals zero. We need two numbers multiplying to six and adding to negative five. These numbers are negative two and negative three.
[Slide 4] Worked Example Step Two
Now we group the terms and take out common factors. This gives us the factored form of the equation. Finally, set each bracket to zero to find x equals two or three.
[Slide 5] Common Mistake Alert
A common mistake is ignoring negative signs while splitting the term. Always verify that your split numbers add up correctly to the middle coefficient. Double check your factorization before solving.
[Slide 6] Quick Recap Summary
To summarize, factorization breaks complex equations into simple linear ones. Use the zero product property to find your solutions. Practice this method for faster board exam solving.