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ADDITION AND SUBTRACTION OF POLYNOMIALS

Pre-Test ( 2 minutes)1. What is the sum of 3x2+ 2x + 1 and 5x -2?b) 3x2 + 7x -1 c) 3x2 - 7x + 1b) -3x2 -3x -1

a) 10x - 1

2. Subtract 2x2 5x + 1 from 5x2 -2x -1

b) 3x2 - 10x -2 c) 3x2 + 3x + 2b) -3x2 + 3x + 2 a) 3x2 - 7x

WRONG

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DDREAMER (D) - TRY AGAIN BABYDDREAMER (D) - WRONG

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In Addition and Subtraction of Polynomials,Similar or Like terms should always be considered

What are Like Terms?Algebraic ExpressionsLike TermsUnlike Termsx , 2x, 3x, 4x2x2, 2y22x, 2y4xy2, xy26b, 6b32x2y, 2xy22xy, -2xy, 3xy, 4yx

Put a check whether the expressions are like terms or unlike termsNote: Only like terms can be added or subtracted

Like Terms or Similar Terms are algebraic expressions with the same variables and exponent regardless of numerical coefficient

Familiarize yourself with the Tiles below:

Stands for +1Stands for -1Stands for +xStands for -xStands for + x2Stands for - x2Can you represent the following quantities using the tiles above?

1. x 2 2. 4x +1 Addition of Polynomials Using Tiles

x 2 Is the same as

4x +1 Is the same as:

Use the tiles to find the sum of the following polynomials; 1. 5x + 3x 2. (3x - 4) - 6x 3. (2x2 5x + 2) + (3x2 + 2x)

5x + 3x

(3x - 4) - 6x

(3x - 4) - 6x = -3x -4

+++===000Recall that combining +x and x will result to zero

(2x2 5x + 2) + (3x2 + 2x)

plus

(2x2 5x + 2) + (3x2 + 2x)

plus

(2x2 5x + 2) + (3x2 + 2x) = 5x2 - 3x + 2

Note: Combining +x and x will result to zero, such that:++== 00

2x2 5x + 23x2 + 2x5x2 - 3x + 2 +Using Paper and PenArrange the expressions according the degree of polynomial from highest to lowest, then arrange like terms in the same column and proceed to operation.ADD (2x2 5x + 2) and (3x2 + 2x)2x25x+23x2+2x+

ADD (2x2 5x + 2) and (3x2 + 2x)or2x2 + 3x2 5x + 2x + 2(2+ 3)x2 +(-5 + 2)x + 2(5)x2 +(-3)x + 25x2 -3x + 2Combine like terms, then add the numerical coefficient

1. Add 4a 3b + 2c, 5a + 8b 10c and -12a + c. More Examples:2. Add 13x4 20x3 + 5x 10 and -10x2 8x4 15x + 10 4a 3b + 2c5a + 8b 10c -12a+ c- 3a5b +-7c13x4 20x3 + 5x 10 8x4 -10x2 15x10 ++5x4-20x3-10x2+20x

2x2 15x + 25 3x2 + 12x 18 -2x2 15x + 25 -3x2 - 12x + 18 +-x2 27x+ 43 Ex. (2x2 15x + 25) (3x2 + 12x 18)Subtraction of Polynomialsor(2x2 15x + 25) (3x2 + 12x 18)2x2 15x + 25 - 3x2 - 12x + 18Remove the parenthesis2x2 - 3x2 - 15x - 12x + 25 + 18Combine like terms(2 3)x2 + (- 15 12)x + (25 + 18)-x2 -27x + 43Add numerical coefficientFinal Answer

2. (30x3 50x2 + 20x 80) (17x3 + 26x + 19) 30x3 50x2 + 20x - 80 -17x3 + 26x + 1930x3 50x2 + 20x - 80 -17x3 - 26x - 19+13x3 50x2 - 6x- 99To subtract polynomials, change the sign of the subtrahend then proceed to the addition rule. Also, remember what subtraction means. It is adding the negative of the quantity. or(30x3 50x2 + 20x 80) (17x3 + 26x + 19) 30x3 50x2 + 20x 80 17x3 -26x -19) 30x3 17x3 + 50x2 + 20x -26x 80 -19 (30-17)x3 + 50x2 + (20 -26)x 99 13x3 + 50x2 -6x 99

Exercises

Author:JESUS M. ABALOSTeacher IMunoz National High SchoolRoxas, Isabela