1. ADDING AND SUBTRACTING POLYNOMIALS

2. REVIEW!

3. A polynomial is a monomial, or sum or difference of monomials. Old Holt 9.1; New Holt 6-4 New Glencoe: 8-1 Add and Subtract Polynomials The degree of a polynomial in one variable is determined by the exponent with the greatest value within the polynomial. The terms of a polynomial may appear in any order. However, in standard form, the terms of a polynomial are ordered form left to right in decreasing order, which means from the greatest exponent to the least. Write 9 + x – 4x 2 in standard form. –4x 2 + x + 9

4. Expression # of Degree Name by Degree Name by Term 12 4x 1 + 3 x 2 – 9 x 2 + 5x + 6 3x 3 + 5x 2 + 10x +5 0 constant monomial 2 quadratic binomial 2 quadratic trinomial 3 cubic polynomial 1 linear binomial The degree of a polynomial, is the greatest degree of any term, in the polynomial; 4x 2 + 3x + 6 Polynomials must be written in standard form; (Hint: in order from the greatest to least degree) Old Holt 9.1; New Holt 6-4 New Glencoe: 8-1 Add and Subtract Polynomials (degree is...two)

5. EXAMPLES

6. (x 2 + 2x 3 – 4) + (3x 2 – 9x + 7) Old Holt 9.1; New Holt 6-4 New Glencoe: 8-1 Add and Subtract Polynomials Find the sum: (4 – 6x – 2x 2 ) + (3x 2 + 5x)

7. FIND THE SUM

8. (4x 2 + 13x – 10) (5x 2 + 10x + 2) – (x 2 – 3x + 12) = Old Holt 9.1; New Holt 6-4 New Glencoe: 8-1 Add and Subtract Polynomials To find the difference: add the opposite, and then combine like terms: (5x 2 + 10x + 2) + (–x 2 + 3x – 12) = (10y 2 – 10y + 16) (16y 2 – 8y + 9) – (6y 2 + 2y – 7) = (16y 2 – 8y + 9) + (–6y 2 – 2y + 7) = (5x 2 + 10x + 2) + (-1)(x 2 – 3x + 12) = (16y 2 – 8y + 9) + (-1)(6y 2 + 2y – 7) =

9. Old Holt 9.1; New Holt 6-4 New Glencoe: 8-1 Add and Subtract Polynomials Find the difference: (2x 2 + 5x) – (–7x – 3) (5x 2 – x) – (x 2 + 3x + 1) (5x + 3) – (6x 3 – 2x 2 )

10. FIND THE DIFFERENCE

11. 3x 2 – 5 x x 2 + 7 C D 2d 2 + d – 4 d 2 + 7 3d 2 – 5d C = 8x 2 – 10x + 14 D = 9d 2 – 9d + 3 3d 2 – 5d FIND THE PERIMETERS: Old Holt 9.1; New Holt 6-4 New Glencoe: 8-1 Add and Subtract Polynomials

12. CHALLENGE. ANSWER THE FOLLOWING: 2x + 5 3x 5x + 4 3x + 2 Old Holt 9.1; New Holt 6-4 New Glencoe: 8-1 Add and Subtract Polynomials 1) Find the perimeter of the large rectangle: 2) Find the perimeter of the small rectangle: 3) Find the difference between the perimeters: 16x + 12 10x + 10 6x + 2