# **Exercise Questions** All questions in this exercise are listed below. Click on a question to view its solution. --- # **Exercise Questions** All questions in this exercise are listed below. Click on a question to view its solution. | Question statement | Link | | ------------------ | ------- | | 1. Factorize $y^3 - 7y - 6$ | [[/content/exercises/class-11/maths/05_Polynomials/5.2 Q-1]] | | 2. Factorize $2x^3 - x^2 - 2x + 1$ | [[/content/exercises/class-11/maths/05_Polynomials/5.2 Q-2]] | | 3. Factorize $2x^3 + 5x^2 - 9x - 18$ | [[/content/exercises/class-11/maths/05_Polynomials/5.2 Q-3]] | | 4. Factorize $3x^3 - 5x^2 - 36$ | [[/content/exercises/class-11/maths/05_Polynomials/5.2 Q-4]] | | 5. Factorize $t^3 + t^2 + 3t - 5$ | [[/content/exercises/class-11/maths/05_Polynomials/5.2 Q-5]] | | 6. Find the other factors of $2x^3 - 15x^2 + 16x + 12$ if $x-2$ is a factor. | [[/content/exercises/class-11/maths/05_Polynomials/5.2 Q-6]] | | 7. Factorize $2x^3 - 15x^2 + 27x - 10$ if $\frac{1}{2}$ is a zero. | [[/content/exercises/class-11/maths/05_Polynomials/5.2 Q-7]] | | 8. Factorize $h(x) = 4x^3 + 4x^2 + 73x + 36$ given $h\left( -\frac{1}{2} \right) = 0$. | [[/content/exercises/class-11/maths/05_Polynomials/5.2 Q-8]] | --- # **Key Concepts** This exercise focuses on the following concepts: - **Factorization**: Breaking down cubic and quadratic expressions into their factors. - **Remainder Theorem**: Using division to find remainders and factors of polynomials. - **Synthetic Division**: A faster method of dividing polynomials to find factors. - **Finding Zeros of Polynomials**: Identifying roots by testing values and dividing polynomials. Understanding these concepts is crucial for solving the exercise questions effectively. --- # **Important Formulas** Below are the key formulas used in this exercise: - **Factor Theorem**: If $x - a$ is a factor of a polynomial, then $P(a) = 0$. - **Synthetic Division**: A method used to divide polynomials and find factors, especially useful for identifying zeros. - **Remainder Theorem**: When dividing $P(x)$ by $x - a$, the remainder is $P(a)$. --- # **Summary** This exercise covers the factorization of polynomials, using both trial and error methods and synthetic division. It helps students understand how to find factors and zeros of polynomials. These methods are useful for simplifying complex polynomial expressions and solving algebraic equations more efficiently. --- # **Reference Videos** ![](https://www.youtube.com/watch?v=xUEI-bMZ6aM&pp=ygUTbmJmIGV4IDUuMiBjbGFzcyAxMQ%3D%3D)