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Adding/Subtracting Ploynomials Powerpoint
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
ADDITION AND SUBTRACTION OF
POLYNOMIALS
Add polynomials.
Simplify the opposite of a polynomial.
Subtract polynomials.
Use polynomials to represent perimeter and
area.
4.4
a
b
c
d
Slide 4- 2 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Objective
Add polynomials.
a
Slide 4- 3 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Example A
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
Slide 4- 4 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
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
Example B
Slide 4- 5 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
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.
Example C
Slide 4- 6 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Objective
Simplify the opposite of a polynomial.
b
Slide 4- 7 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
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.
Slide 4- 8 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Simplify: (8x4 x3 + 9x2 2x + 72)
Solution
(8x4 x3 + 9x2 2x + 72)
= 8x4 + x3 9x2 + 2x 72
Example D
34
34
34
Slide 4- 9 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Objective
Subtract polynomials.
c
Slide 4- 10 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Subtraction of Polynomials
We can now subtract one polynomial from another by
adding the opposite of the polynomial being
subtracted.
Slide 4- 11 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
(10x5 + 2x3 3x2 + 5) (3x5 + 2x4 5x3 4x2)
Solution
(10x5 + 2x3 3x2 + 5) (3x5 + 2x4 5x3 4x2)
= 10x5 + 2x3 3x2 + 5 + 3x5 2x4 + 5x3 + 4x2
= 13x5 2x4 + 7x3 + x2 + 5
Example E Subtract:
Slide 4- 12 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Subtract: (8x5 + 2x3 10x) (4x5 5x3 + 6)
Solution
(8x5 + 2x3 10x) (4x5 5x3 + 6)
= 8x5 + 2x3 10x + (4x5) + 5x3 6
= 4x5 + 7x3 10x 6
Example F
Slide 4- 13 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Write in columns and subtract:
(6x2 4x + 7) (10x2 6x 4)
Solution
6x2 4x + 7
(10x2 6x 4)
4x2 + 2x + 11
Example G
Remember to change
the signs
Slide 4- 14 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Objective
Use polynomials to represent
perimeter and area.
d
Slide 4- 15 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
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.
Example H
w ft
w ft
7 ft
5 ft
Slide 4- 16 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
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.
continued
Slide 4- 17 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Section 4.4
1. Add: (6x5 – x3 + 4x2 + x) +
(x4 – x3 + 8x2 – x + 2).
a) 7x5 – 2x3 + 12x2 + 2x + 2
b) 6x5 + x4 – 2x3 + 12x2 + 2
c) 7x5 – 2x3 + 12x2 + 2
d) 6x5 + x4 + 12x2 + 2
Slide 4- 18 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Section 4.4
1. Add: (6x5 – x3 + 4x2 + x) +
(x4 – x3 + 8x2 – x + 2).
a) 7x5 – 2x3 + 12x2 + 2x + 2
b) 6x5 + x4 – 2x3 + 12x2 + 2
c) 7x5 – 2x3 + 12x2 + 2
d) 6x5 + x4 + 12x2 + 2
Slide 4- 19 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Section 4.4
2. Subtract: (1.1x3 – 8x2 + 4.5x) –
(3x3 – x2 + 0.5x – 6).
a) –2.2x3 – 7x2 + 4x + 6
b) –1.9x3 – 7x2 + 4x + 6
c) –2.9x3 – 7x2 + 4x + 6
d) –1.9x3 – 9x2 + 4x + 6
Slide 4- 20 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Section 4.4
2. Subtract: (1.1x3 – 8x2 + 4.5x) –
(3x3 – x2 + 0.5x – 6).
a) –2.2x3 – 7x2 + 4x + 6
b) –1.9x3 – 7x2 + 4x + 6
c) –2.9x3 – 7x2 + 4x + 6
d) –1.9x3 – 9x2 + 4x + 6