Q1. In the formula p(x) = g(x)q(x) + r(x), which represents the dividend?
✔ p(x) is the polynomial being divided, known as the dividend.
Q2. What is the condition for the degree of the remainder r(x)?
✔ The degree of the remainder must be strictly less than the divisor.
Q3. What was the remainder in our worked example?
✔ The polynomial divided exactly, resulting in a zero remainder.
Show transcript
[Slide 1] Intuition Behind Division
Think about how you divide numbers. Polynomials follow the exact same structure. The dividend is split into a product and a leftover part.
[Slide 2] The Division Algorithm Formula
Here is the formal rule you must memorize. The remainder degree is always smaller than the divisor. This ensures the division process stops correctly.
[Slide 3] Worked Example Setup
Consider this specific cubic polynomial for our example. We are dividing it by the linear term x minus two. Let us set up the long division process.
[Slide 4] Worked Example Solution
After performing the long division steps carefully, we get this quotient. The remainder is zero because it divides perfectly. You can multiply back to check your answer.
[Slide 5] Common Student Mistake
Students often stop when the remainder is wrong. Ensure the remainder degree is strictly less than divisor. Also watch out for negative signs in subtraction.
[Slide 6] Quick Recap and Tips
Remember this relationship is key for CBSE questions. Always verify your result using the algorithm equation. Practice different types of polynomials to gain speed.