ALGEBRAIC EXPRESSIONS Presented to Farjana Siddiqua Faculty Department of MAT Presented By Md. Zahidul Alam Sec:A Program: BBA Course code: MAT 107 Basic Mathematics Group: YOUTH POWER

Evaluation Of Algebraic Expressions We have learned that, in in an algebraic expression, letters can stand for numbers. When we substitute a specific value for each variable, and then perform the operations, it's called evaluating the expression. The most common "expression" you'll likely need to evaluate will be polynomials. To evaluate, you take the polynomial and plug in a value for x. # Evaluate 𝑥 4 + 3 𝑥 3 – 𝑥 2 + 6 for x = –3 (–3)4 + 3(–3)3 – (–3)2 + 6 = 81 + 3(–27) – (9) + 6 = 81 – 81 – 9 + 6 = –3 (Ans: -3)

Algebraic Terms And Expressions Constants, variables, and combinations of constants and variables formed by taking products and quotients are called Algebraic Terms. Algebraic Terms: 5X - 3

Algebraic Terms And Expressions Algebraic terms, sums and differences of algebraic terms, and quotients of sums and differences of algebraic terms are called Algebraic Expressions. Algebraic Expressions:

The Definition Of A Polynomial A polynomial is a monomial or the sum or difference of monomials. Each monomial is called a term of the polynomial. Important!: Terms are separated by addition signs and subtraction signs, but never by multiplication signs. Examples of polynomials: Polynomial Number of terms Some examples Monomial 1 2, x, 5 𝑥 2 Binomial 2 2x + 5, 𝑥 3 - 5, x - 5 Trinomial 3 𝑥 2 + 5x + 6, 𝑥 3 - 3x + 8 Only whole number are Polynomial. Negative exponent, denominator are not polynomial.

Degree Of A Monomial The Degree of a Monomial is the sum of the exponents on the variables in the Monomial. The degree of a monomial is the sum of the exponents of all its variables:

Degree Of A Polynomial The Degree of a Polynomial is the degree of the highest degree term in the Polynomial. The degree is the term with the greatest exponent Recall that for y2, y is the base and 2 is the exponent.

The Addition And Subtraction Of Polynomials Adding (or subtracting) polynomials is really just an exercise in collecting like terms. For example, if we want to add the polynomial. # 2 𝑥 2 + 4x – 3 to the polynomial 6x + 4 we would just put them together and collect like terms: (2 𝑥 2 + 4x – 3) + (6x – 4) = 2 𝑥 2 + 4x – 3 + 6x – 4 = 2 𝑥 2 + 10x – 7

The Multiplication And Division Of Algebraic Terms The Multiplication of polynomials will require the use of the laws of exponents. So we will first discuss the laws of exponents and demonstrate their use in the multiplication and division of Algebraic Terms. We can multiply two algebraic terms to get a product, which is also an algebraic term. Example : Evaluate 3p 𝑞 3 × 4qr Solution: 3p 𝑞 3 × 4qr = 3 × p × q × q × q × 4 × q × r = 3 × 4 × p × q × q × q × q × r = 12 × p × 𝑞 4 × r = 12p 𝑞 4 r We can divide an algebraic term by another algebraic term to get the quotient. The steps below show how the division is carried out. Example : Evaluate 6p 𝑞 3 ÷ 3pq Solution: 6p 𝑞 3 ÷ 3pq = 6 ×𝑝 × 𝑞 × 𝑞 × 𝑞 3 ×𝑝 ×𝑞 = 2 𝑞 2

The Multiplication Of Polynomials There were two formats for adding and subtracting polynomials: "horizontal" and "vertical". You can use those same two formats for multiplying polynomials. The very simplest case for polynomial multiplication is the product of two one-term polynomials. There is 2 method…… EX: Horizontal method & Vertical method. Horizontal method: Example: Evaluate –3x(4 𝑥 2 – x + 10) To do this, We have to distribute the –3x through the parentheses: –3x(4 𝑥 2 – x + 10) = –3x(4 𝑥 2 ) – 3x(–x) – 3x(10) = –12 𝑥 3 + 3 𝑥 2 – 30x

Vertical method:

ANY QUESTION????