ADDITION AND SUBTRACTION OF POLYNOMIALS

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Presentation transcript:

ADDITION AND SUBTRACTION OF POLYNOMIALS 4.4 ADDITION AND SUBTRACTION OF POLYNOMIALS a. Add polynomials. b. Simplify the opposite of a polynomial. c. Subtract polynomials. d. Use polynomials to represent perimeter and area.

Add. (6x3 + 7x  2) + (5x3 + 4x2 + 3) Solution (6x3 + 7x  2) + (5x3 + 4x2 + 3) = (6 + 5)x3 + 4x2 + 7x + (2 + 3) = x3 + 4x2 + 7x + 1

Add: (3  4x + 2x2) + (6 + 8x  4x2 + 2x3) Solution (3  4x + 2x2) + (6 + 8x  4x2 + 2x3) = (3  6) + (4 + 8)x + (2  4)x2 + 2x3 = 3 + 4x  2x2 + 2x3

Add: 10x5  3x3 + 7x2 + 4 and 6x4  8x2 + 7 and 4x6  6x5 + 2x2 + 6 Solution 10x5  3x3 + 7x2 + 4 6x4  8x2 + 7 4x6  6x5 + 2x2 + 6 4x6 + 4x5 + 6x4  3x3 + x2 + 17 The answer is 4x6 + 4x5 + 6x4  3x3 + x2 + 17.

Opposites of Polynomials To find an equivalent polynomial for the opposite, or additive inverse, of a polynomial, change the sign of every term. This is the same as multiplying by 1.

Simplify: (8x4  x3 + 9x2  2x + 72) Solution (8x4  x3 + 9x2  2x + 72) = 8x4 + x3  9x2 + 2x  72

Subtraction of Polynomials We can now subtract one polynomial from another by adding the opposite of the polynomial being subtracted.

(10x5 + 2x3  3x2 + 5)  (3x5 + 2x4  5x3  4x2) Solution = 10x5 + 2x3  3x2 + 5 + 3x5  2x4 + 5x3 + 4x2 = 13x5  2x4 + 7x3 + x2 + 5

Solution (8x5 + 2x3  10x)  (4x5  5x3 + 6) Subtract: (8x5 + 2x3  10x)  (4x5  5x3 + 6) Solution (8x5 + 2x3  10x)  (4x5  5x3 + 6) = 8x5 + 2x3  10x + (4x5) + 5x3  6 = 4x5 + 7x3  10x  6

Write in columns and subtract: (6x2  4x + 7)  (10x2  6x  4) Solution 6x2  4x + 7 (10x2  6x  4) 4x2 + 2x + 11 Remember to change the signs

1. Familiarize. We make a drawing of the situation as follows. A 6-ft by 5-ft hot tub is installed on an outdoor deck measuring w ft by w ft. Find a polynomial for the remaining area of the deck. Solution 1. Familiarize. We make a drawing of the situation as follows. w ft 7 ft 5 ft

continued 2. Translate. Rewording: Area of Area of Area deck  tub = left over Translating: w ft  w ft  5 ft  7 ft = Area left over 3. Carry out. w2 ft2  35 ft2 = Area left over. 4. Check. As a partial check, note that the units in the answer are square feet, a measure of area, as expected. 5. State. The remaining area in the yard is (w2  35)ft2.