Polynomials 9-3-15

Examples: Polynomials Monomials: 4f 3x3 4g2 2 Binomials: 4t + 9 9 – 7g 5x2 + 7x 6x3 – 8x Trinomials: x2 + 2x + 3 5x2 – 6x – 1 y4 + 15y2 + 100 Polynomials: x3 – 3x2 + 3x – 9 p4 + 2p3 + p2 + 9p - 5 Polynomials are algebraic expressions. This group of expressions include monomials, binomials, trinomials. Monomials: contain ONE term Binomials: contain TWO terms Trinomials: contain THREE *Any expression with more than three terms is just called a polynomial. **REMEMBER: TERMS are separated by the operation symbols.

Specifics of a Polynomial Degree: the exponent of the variable Degree of the Polynomial: Highest (largest) exponent of the polynomial Standard Form: Terms are placed in descending order by the DEGREE Leading Coefficient: Once in standard form, it’s the 1st NUMBER in front of the variable (line leader) k + 4 2x2 – 9x +7 6y3 – 5y2 - y

Special Kinds of Polynomials Degree (Largest Exponent) Name by Degree Constant 1 Linear 2 Quadratic

Special Names -2y -9 Degree: 1 Degree Name: Linear # of Terms Name: Binomial Leading Coefficient: -2

Degree Name: Quadratic # of Terms Name: Trinomial Special Names 4x2 + 3x -7 Degree: 2 Degree Name: Quadratic # of Terms Name: Trinomial Leading Coefficient: 4

Adding Polynomials When adding polynomials, make sure the exponents are variables are the same on the terms you are combining. The easiest way to do this is to line them up in columns. Example: Add 3x2 + 14 and 5x2 + 2x 3x2 + 0x + 14 + 5x2 + 2x + 0 ____________ 8x2 + 2x + 14

Adding Polynomials Examples: Add (4x3 – 2x) + (-x3 - 4) 4x3 – 2x + 0 + - x3 + 0x – 4 _______________ 3x3 + 2x – 4 You try: 3y2 + 8y + 2 and 2y2 + 5 (y2 + 3y – 7) + (2y2 - y + 8) -2p + 3 and 9p2 – p + 4 12c2 – 10c + 6 and -3c2 + 2c – 6 (-4x2 + 5x – 7) + (8x2 – 7)

Subtracting Polynomials When you subtract polynomials, it is important to remember to change ALL the signs in the subtracted polynomial (the one listed second) and then add. Example: (4y2 + 8y + 9) – (2y2 + 6y - 4) Change every sign in the second set of parentheses (4y2 + 8y +9) + (-2y2 – 6y + 4) Now add. 4y2 + 8y + 9 + -2y2 – 6y + 4 ____________ 2y2 + 2y + 13

Subtracting Polynomials Example: Add (4x3 – 2x) - (-x3 - 4) Change every sign in the second set of parentheses (4x3 – 2x) + ( x3 + 4) Now add. 4x3 – 2x + 0 + x3 + 0x + 4 _______________ 5x3 - 2x + 4 You try: (3y2 + 8y + 2) – (2y2 + 5) (y2 + 3y – 7) - (2y2 - y + 8) (-2p + 3) - (9p2 – p + 4) (12c2 – 10c + 6) – ( -3c2 + 2c – 6) (-4x2 + 5x – 7) - (8x2 – 7)

Ticket out the Door Add. Subtract. (11t3 – 4t2 + 3) + (-t3 + 4t2 – 5) (3p2 + 2p – 1) – (-5p2 – p +8)