Polynomial Formula Class 9
Polynomials with lower degrees like linear and quadratic polynomials can be solved in a few simple steps. But determining the roots of higher-order polynomials may involve a multi-step process requiring various polynomial formulas. Polynomial formulas class 9 help us in solving these polynomial equations to derive their roots. Students can find the list of these fundamental polynomial formulas along with some useful tips to memorize them.
List of Polynomial Formula Class 9
Here is a brief list of important polynomial formulas that are applicable in finding the roots of polynomial equations.
- (x + y)2 = x2 + 2xy + y2
- (x – y)2 = x2 – 2xy + y2
- (x + y) (x – y) = x2 - y2
- (x + a) (x + b) = x2 + (a + b) x + ab.
- (x + a) (x – b) = x2 + (a – b) x – ab.
- (x – a) (x + b) = x2 + (b – a) x – ab.
- (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx
- (x + y)3 = x3 + y3 + 3xy(x + y)
- (x – y)3 = x3 – y3 – 3xy(x – y)
- x3 + y3 + z3 – 3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz – zx)
Applications of Polynomial Formulas Class 9
Polynomial Formulas Class 9 are applied in several things in our daily life. There are various routine computations that can be represented as polynomials. We make use of these polynomials without even realizing it during driving, shopping, banking, etc. Some of the prominent applications of polynomial formulas are as follows:
- Polynomial formulas class 9 are useful in construction work, business, implementation of traffic lights, etc. Mathematical applications of polynomial formulas include the representation of the perimeter, area, and volume of geometric figures.
- Polynomial formulas are applied in various subjects like physics and chemistry. In physics, polynomials are used to measure acceleration and represent units of energy, electricity, etc.
- In chemistry, these polynomial formulas are used to compose and balance chemical equations.
- In economics, polynomial formulas are used in modeling stock markets, expense budgeting, etc.
Tips to Memorize Polynomial Formulas Class 9
The students must make sure to understand the meaning of these terms first before moving ahead to memorize the formulas. They can get help from teachers or their friends to get clarity on the same.
- After having crystal clear knowledge of the terms used in formulas students can try to use some fun tricks like phrases to remember them better.
- Students can download and set the polynomial formula images as wallpaper on their devices which will help them ensure a quick revision while they are using their mobiles, tablets or laptops.
- Students should practice lots and lots of problems and examples given in the textbook. It will provide optimal coverage of the usage of formulas in different contexts.
Polynomial FormulaClass 9 Examples
Example: Determine y + 1 is a factor of y3 + y2 + y + 1
Solution: When a polynomial p(y) is divided by (y - a) and if p(a) = 0 then (y - a) is a factor of p(y).
The root of y + 1 = 0 is -1.
Let p(y) = y3 + y2 + y + 1
Therefore, p(-1) = (-1)3 + (-1)2 + (-1) + 1
⇒ -1 + 1 - 1 + 1 = 0
Since the remainder of p(-1) is 0, we conclude that y + 1 is a factor of y3 + y2 + y + 1.
Students can download the printable Maths formulas Class 9 sheet from below.
FAQs On Polynomials Formula Class 9
What are the Important Polynomial Formulas Class 9?
The important polynomial formulas class 9 are as below:
- (a + b)2 = a2 + 2ab + b2
- (a + b) (a – b) = a2 - b2
- (x + a) (x + b) = x2 + (a + b) x + ab.
- (a – b)2 = a2 – 2ab + b2
- (x + a) (x – b) = x2 + (a – b) x – ab.
- (x – a) (x + b) = x2 + (b – a) x – ab.
How are Polynomial Formula Class 9 Applied in Real Life?
The use of Polynomial formulas class 9 can be seen in a wide variety of practical situations and studies including subjects like economics, chemistry, and physics. Polynomial formulas are also applied in physics and chemistry. For instance, in physics polynomial formulas are used to represent units of energy and measure acceleration. The use of polynomial formulas can also be seen in chemistry to write or balance various chemical equations.
What Formula is used to Solve Quadratic Polynomials?
The formula to solve quadratic polynomials is x = − b ± √b2− 4ac/2a. A quadratic polynomial is a polynomial which is in the form of ax² + bx + c where a, b and c are real numbers. Since the square roots cannot be defined for the negative numbers in the real number system if b² - 4ac < 0 the quadratic equation will have no real roots.
Why is it Important to Solve Questions Based on the Class 9 Polynomial Formula?
Solving questions based on Class 9 Polynomial Formulas will help students in reinforcing knowledge of the algebraic entities, expressions, and their definitions like coefficients, variables, linear polynomials, quadratic polynomials, roots and many more. These formulas help in finding the roots of different types of polynomials. While attempting questions based on these formulas, students will develop excellent algebraic skills required for higher studies and competitive exams. Hence students must practice all the questions based on class 9 polynomial formulas.
How to Download the Polynomial Formula Class 9 pdf?
To download the polynomial formula class 9 pdf students can tap on the download pdf option provided on this page. On clicking the given option a popup will appear to enter your mobile number. Enter mobile number and OTP received to download the formula sheet.