Operations on Polynomials

Adding and Subtracting Polynomials

Adding Polynomials ,[object Object],+ + + = = 2 2 2 Does not =

Example ,[object Object],(-7z 2 + 9z – 3) + (8z 2 – 6z + 9) = -7z 2 + 8z 2 + 9z – 6z – 3 + 9 = 1z 2 + 3z + 6 = z 2 + 3z + 6 Rearrange the terms so that the like terms are grouped together. Add like terms. 1z 2 = z 2

Finding the Opposite of a Polynomial ,[object Object]

Example ,[object Object],– (–5a + 3b – 7c) = We change the sign of each term 5a 3b 7c – + – in front of parentheses

Subtracting Two Polynomials ,[object Object]

Example ,[object Object],[object Object],= 3a 2 + 4a – 7 + ( – 7a 2 ) + 2a + 5 A – sign in front of parentheses indicates we are subtracting. We change the sign of terms that were inside parentheses, then add. = 3a 2 + 4a – 7 + (– 7a 2 ) + 2a + 5 Simplify by combining like terms. = -4a 2 + 6a – 2

Example ,[object Object],-2y (5y 2 + 3y – 8) = -2y (5y 2 ) – 2y (3y) – 2y (– 8) Multiply each term by -2y = -10y 3 – 6y 2 + 16y

Example ,[object Object],First F Outer O Inner I Last L 3x 2 - 6x x - 2 (3x + 1)(x – 2) = 3x 2 – 5x - 2 Combine like terms. (3x + 1) (x - 2) First Outer Inner Last

I hope you enjoyed this short presentation on Polynomials

Operations on Polynomials

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