PolynomialsMade by: Shivam Saxena

Class : 10th ‘B’Subject : Maths

Evaluating Polynomials

ExamplesFind the value of 2x3 – 3x + 4 when x =

2.2 x 3 – 3 x + 4= 2( 2 ) 3 – 3 ( 2 ) + 4

= 2 ( 8 ) + 6 + 4= - 16 + 10

= - 6

VocabularyMonomial: A number, a variable or the product of a number and one or more variables.Polynomial: A monomial or a sum of monomials.

Binomial: A polynomial with exactly two terms.

Trinomial: A polynomial with exactly three terms.

Coefficient: A numerical factor in a term of an algebraic expression.

VocabularyDegree of a monomial: The sum of the exponents of all of the variables in the monomial.

Degree of a polynomial in one variable: The largest exponent of that variable.

Standard form: When the terms of a polynomial are arranged from the largest exponent to the smallest exponent in decreasing order.

Polynomials on one variable 1. A polynomial is a monomial or the sum of monomials

24x 83 3 x 1425 2 xx2 . Each monomial in a polynomial is a term of the polynomial.

A. The number factor of a term is called the coefficient.B. The coefficient of the first term in a polynomial is the lead coefficient.

3. A polynomial with two terms is called a binomial.4. A polynomial with three terms is called a trinomial.

ExamplesWrite the polynomials in standard form.

745 24 xxx

44x 2x x5 7

)7552(1 234 xxxx

4x 32x 25x x5 7

Remember: The lead coefficient

should be positive in standard form.

To do this, multiply the polynomial by –1 using the distributive

property

243 5572 xxxx

4x 32x 25x x5 7

Practice 1Write the polynomials in standard form and identify the polynomial by degree and number of terms.

23 237 xx

xx 231 2

23 237 xx

33x 22x 7

7231 23 xx

723 23 xx

This is a trinomial. The trinomial’s degree is 3.

Problem 2

Find the Sum

Add (x2 + x + 1) to (2x2 + 3x + 2)

You might decide to add like terms as the next slide demonstrates.

Add Like Terms

x2 + x + 1+ 2x2 + 3x + 2 = 3x2+ 4x+3

Or you could add the trinomials in a column

D i v i d i n g P o l y n o m i a l s

Dividing a polynomial by a polynomial other than a monomial uses a “long division” technique that is similar to the process known as long division in dividing two numbers, which is reviewed on the next slide.

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