Polynomials : a polynomial is an expression made of using two or more terms.
Types of polynomials - polynomials 3 different types
Monomial - It is a polynomial with one term. hence the name “ mono”. For example 4X
Binomial - It is a polynomial with two unlike terms. hence the name “ bi”. For example 3X+4Y
Trinomial - It is a polynomial with three unlike terms. hence the name “ tri” . For example 3X+7Y+2Z
Degrees of polynomial : The highest exponents or powers of that expression Is called degree of polynomial.
For example : 3X^2+4Y+5 —- This has 3 terms 3X^2 , 4y, 5. So it is a trinomial.
Terms : A term is a single mathematical expression. it may be a single number( positive or negative) and a single variable. A term is usually separated by + / - sign.
For example:
4X-6Y+10 — There are three terms in this expression, 4X, -6Y , 10
3Yx 4Z-6 – There are two terms in this expression, 3Yx4Z = 12YZ ; _-6
Coefficient : in mathematics a coefficient is a multiplicative factor. that is a number multiplied by a variable
For example :
6X+2 – The coefficient of X is 6
3X-4Y+20 — The coefficient of X is 3; the coefficient of Y is -4
Polynomials in one variable
Polynomial in one variable is an algebraic expressions that consist of terms in the form of axn . Where n is a non negative integer (ie either positive or negative) And is a real number and is also called the coefficient of the term. the degree of the polynomial in one variable is the largest exponent in the polynomial.
if the variable in the polynomial is X then we did not denote it as P(X) OR Q(X) .
Example:
1) 5X3 + 4X2 - 8X +4 Is a one variable polynomial as it has only one variable X .
2) 6Y2+ 3Y - 4 Is a one variable polynomial as it has only one variable Y.
Degrees of polynomial :
Highest power of a variable in a polynomial is called the degree of polynomial.
Example:
4Y3 + 3Y2 +7Y +2 Is a One variable polynomial with degree 3. As the highest power is 3.
43+ 73X + 4X2 + 3X3 + 83X5 Is a one variable polynomial with degree 5. As the highest power is 5.
Based on the degree of polynomial the polynomials in one variable can be classified as
Zero polynomial
linear polynomial
quadratic polynomial
cubic polynomial
zero polynomial:
if the degree of the polynomial is zero (0), then it is a zero polynomial. Usually zero polynomials are only constant.
Example: 1) 2x0 + 5 = 2(1) + 5 (x0=1)
= 2+5
= 7
2) 5y0+ 2 = 5(1) +2 (x0 = 1)
= 5+2
= 7
Linear polynomial: If the degree of the polynomial is 1 then the polynomial is called linear polynomial. The linear polynomial has only one solution as it has only one variable. For example
3x+ 4
z+3
Quadratic polynomial: a polynomial with the highest degree of 2 is called a quadratic polynomial. a quadratic polynomial in one variable has only two solutions. For example:
4x2 +7
3y2+ 4y - 5
Cubic polynomial: A polynomial with the highest degree 3 is called a cubic polynomial. a cubic polynomial has exactly 3 solutions.
For example:
7x3+ 8x2 -5
3y3 -8
Like terms unlike terms
Like terms- In Algebra Like terms are defined as the terms with the same variable which is raised to the same power. In like terms only the coefficient can vary .
For example: 3Y +9y ; 14b²+18b²
Unlike terms- in Algebra and like terms are defined as the terms with different variables or which are raised to different powers.
For example; 4Y+9Z; 4XY²-3X²Y
Identify like terms:
3Y ² , 2Y , 4Y² ,6Y = (3Y²,4Y²) , (2Y,6Y)
5X²Y , -3YX² , 8XY² , 9XY² = (5X²Y , -3YX²) , ( 8XY² , 9XY²)
Addition and subtraction of like terms:
when adding or subtracting like terms only the coefficients are added or subtracted the variable will remain the same.
for example:
1) 3X+5Y+2X-3X+6y
STEP1 - Combine like terms together.
(3X+2X-
STEP2 - Combine the coefficient.
(3+2-3)X + (5+6) Y = 2X+11Y
2) 5X²Y-3XY²+7X²Y+9XY²
STEP1 - Combine like terms together.
(5x²y+7x²y)
STEP2 - Combine the coefficient.
(5+7)X²Y+(
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