An expression which is the sum of terms of the form a x k where k is a nonnegative integer is a polynomial. Polynomials are usually written in standard.

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Presentation transcript:

An expression which is the sum of terms of the form a x k where k is a nonnegative integer is a polynomial. Polynomials are usually written in standard form. Polynomials What is POLYNOMIAL?

Standard form means that the terms of the polynomial are placed in descending order, from largest degree to smallest degree. Polynomial in standard form: 2 x 3 + 5x 2 – 4 x + 7 Degree Constant termLeading coefficient Polynomials

The degree of each term of a polynomial is the exponent of the variable. The degree of a polynomial is the largest degree of its terms. When a polynomial is written in standard form, the coefficient of the first term is the leading coefficient. Polynomials

A polynomial with only one term is called a monomial. A polynomial with two terms is called a binomial. A polynomial with three terms is called a trinomial. Polynomials Kinds of Polynomials (according to number of terms)

Find the sum. Write the answer in standard format. (5x 3 – x + 2 x 2 + 7) + (3x – 4 x) + (4x 2 – 8 – x 3 ) Adding Polynomials SOLUTION Vertical format: Write each expression in standard form. Align like terms. 5x x 2 – x + 7 3x 2 – 4 x + 7 – x 3 + 4x 2 – 8 + 4x 3 + 9x 2 – 5x + 6

Find the sum. Write the answer in standard format. (2 x 2 + x – 5) + (x + x 2 + 6) Adding Polynomials SOLUTION Horizontal format: Add like terms. (2 x 2 + x – 5) + (x + x 2 + 6) =(2 x 2 + x 2 ) + (x + x) + (–5 + 6) =3x x + 1

Find the difference. (–2 x 3 + 5x 2 – x + 8) – (–2 x 2 + 3x – 4) Subtracting Polynomials SOLUTION Use a vertical format. To subtract, you add the opposite. This means you multiply each term in the subtracted polynomial by –1 and add. –2 x 3 + 5x 2 – x + 8 –2 x 3 + 3x – 4– Add the opposite No change –2 x 3 + 5x 2 – x x 3 – 3x + 4 +

Find the difference. (–2 x 3 + 5x 2 – x + 8) – (–2 x 2 + 3x – 4) Subtracting Polynomials SOLUTION Use a vertical format. To subtract, you add the opposite. This means you multiply each term in the subtracted polynomial by –1 and add. –2 x 3 + 5x 2 – x + 8 –2 x 3 + 3x – 4– 5x 2 – 4x + 12 –2 x 3 + 5x 2 – x x 3 – 3x + 4 +

Find the difference. (3x 2 – 5x + 3) – (2 x 2 – x – 4) Subtracting Polynomials SOLUTION Use a horizontal format. (3x 2 – 5x + 3) – (2 x 2 – x – 4)= (3x 2 – 5x + 3) + (–1)(2 x 2 – x – 4) = x 2 – 4x + 7 = (3x 2 – 5x + 3) – 2 x 2 + x + 4 = (3x 2 – 2 x 2 ) + (– 5x + x) + (3 + 4)