Chapter 2: Polynomials

Class 9 Maths Chapter 2 on Polynomials includes definitions, the Remainder Theorem, Factor Theorem, and algebraic expressions. These questions are very important for examinations.

  • To know your total score, there is a button at the bottom of the last question. Click it to know your score.
  • There is no negative marking.

2892

1. One of the zeroes of the polynomial $2 x^{2}+7 x-4$ is

2895

2. $x+1$ is a factor of the polynomial

2886

3. Degree of the zero polynomial is

2885

4. Degree of the polynomial $4 x^{4}+0 x^{3}+0 x^{5}+5 x+7$ is

2894

5. If $x+1$ is a factor of the polynomial $2 x^{2}+k x$, then the value of $k$ is

2896

6. One of the factors of $\left(25 x^{2}-1\right)+(1+5 x)^{2}$ is

2890

7. Zero of the zero polynomial is

2899

8. Which of the following is a factor of $(x+y)^{3}-\left(x^{3}+y^{3}\right)$ ?

2883

9. Which one of the following is a polynomial?

2882

10. If $x^{2}+k x+6=(x+2)(x+3)$ for all $x$, then the value of $k$ is

2903

11. If $a+b+c=0$, then $a^{3}+b^{3}+c^{3}$ is equal to

2898

12. The factorisation of $4 x^{2}+8 x+3$ is

2897

13. The value of $249^{2}-248^{2}$ is

2888

14. The value of the polynomial $5 x-4 x^{2}+3$, when $x=-1$ is

2900

15. The coefficient of $x$ in the expansion of $(x+3)^{3}$ is

Important Definitions and Theorems

Polynomial:
A polynomial is a mathematical expression that consists of variables and coefficients. It can have one or more terms.

Factor Theorem:
According to the Factor Theorem, if $P(x)$ is a polynomial and $a$ is a root, then $(x - a)$ is a factor of the polynomial.

Remainder Theorem:
The Remainder Theorem states that when a polynomial $P(x)$ is divided by another polynomial $d(x)$, the remainder is what remains after the division.

Main Concepts and Formule Chapter 2 Class 9 Mathematics

Algebraic identities -
$(x+y)^{2}=x^{2}+2 x y+y^{2}$
$(x-y)^{2}=x^{2}-2 x y+y^{2}$
$x^{2}-y^{2}=(x+y)(x-y)$
$(x+a)(x+b)=x^{2}+(a+b) x+a b$
$(x+y+z)^{2}=x^{2}+y^{2}+z^{2}+2 x y+2 y z+2 z x$
$(x+y)^{3}=x^{3}+3 x^{2} y+3 x y^{2}+y^{3}=x^{3}+y^{3}+3 x y(x+y)$
$(x-y)^{3}=x^{3}-3 x^{2} y+3 x y^{2}-y^{3}=x^{3}-y^{3}-3 x y(x-y)$
$x^{3}+y^{3}=(x+y)\left(x^{2}-x y+y^{2}\right)$
$x^{3}-y^{3}=(x-y)\left(x^{2}+x y+y^{2}\right)$
$x^{3}+y^{3}+z^{3}-3 x y z=(x+y+z)\left(x^{2}+y^{2}+z^{2}-x y-y z-z x\right)$

Algebraic expressions are formed using constants, variables, and operators. They can represent a polynomial and can undergo operations like addition, subtraction, multiplication, and division.

Conclusion

The Chapter 2: Polynomials of Class 9 Maths strengthens the foundational understanding of polynomials. It includes essential concepts and questions that are useful for exams.