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9.1 Adding and Subtracting Polynomials. Objective: The learner will..,. NCSCOS. Write polynomials in standard form, Add and Subtract polynomials, by combining or subtracting like terms. 1.01. 9.1 Adding and Subtracting Polynomials. Identify each polynomial by the name and degree. 12.

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Objective: The learner will..,

NCSCOS

• Write polynomials in standard form,
• Add and Subtract polynomials, by combining or subtracting like terms
• 1.01

Identify each polynomial by the name and degree

12

monomial constant

8x – 5

binomial linear

4x + 3

binomial linear

x2 + 6

3x2 + 6x + 5

x3 + 2x – 2

trinomial cubic

x3 + 4

binomial cubic

Standard form: the terms of the polynomial are in descending order, meaning, the greatest exponent to the smallest (left to right).

2x2 + 7

x3 + 6x2

6x2 + x3

-4x2 + x + 9

9 + x – 4x2

a + a2 + a3 + 1

a3 + a2 + a + 1

8 – 3m2 – m3 + 2m

– m3 – 3m2 + 2m + 8

in horizontal form:

(x2 + 2x + 5) + (3x2 + x + 12)

= 4x2 + 3x + 17

in vertical form:

x2 + 2x + 5

+

3x2 + x + 12

= 4x2 + 3x + 17

3x2 – 4x + 8

x2 + x + 1

Simplify:

+ 2x2 – 7x – 5

+ 2x2 + 3x + 2

5x2 – 11x + 3

3x2 + 4x + 3

(4b2 + 2b + 1)

+ (7b2 + b – 3)

a2 + 8a – 5

+ 3a2 + 2a – 7

11b2 + 3b – 2

4a2 + 10a – 12

7d2 + 7d

z2 + 5z + 4

Simplify:

+ 2d2 + 3d

+ 2z2 - 5

9d2 + 10d

3z2 + 5z – 1

(2x2 – 3x + 5)

+ (4x2 + 7x – 2)

(a2 + 6a – 4)

+ (8a2 – 8a)

9a2 – 2a – 4

6x2 + 4x + 3

3d2 + 5d – 1

7p2 + 5

Simplify:

+ (–4d2– 5d + 2)

+ (–5p2– 2p + 3)

–d2 + 1

2p2– 2p + 8

(3x2 + 5x)

+ (4 – 6x – 2x2)

(x3 + x2 + 7)

+ (2x2 + 3x – 8)

x2– x + 4

x3 + 3x2 + 3x – 1

Simplify:

4p2 + 5p

2x3 + x2 – 4

+ (-2p + p + 7)

+ 3x2 – 9x + 7

4p2 + 4p + 7

2x3 + 4x2 – 9x + 3

5y2 – 3y + 8

+ 4y3 – 9

(8cd – 3d + 4c)

+ (-6 + 2cd – 4d)

4y3 + 5y2 – 3y – 1

4c – 7d + 10cd – 6

Simplify:

(12y3 + y2 – 8y + 3) + (6y3 – 13y + 5)

(7y3 + 2y2 – 5y + 9) + (y3 – y2 + y – 6)

(6x5 + 3x3 – 7x – 8) + (4x4 – 2x2 + 9)

= 18y3 + y2 – 21y + 8

= 8y3 + y2 – 4y + 3

= 6x5 + 4x4 + 3x3 – 2x2 – 7x + 1

Subtracting Polynomials (Note: subtraction is adding the opposite)

(5x2 + 10x + 2) – (x2 – 3x + 12)

(5x2 + 10x + 2) + (–x2) + (3x) + (–12)

= 4x2 + 13x – 10

5x2 + 10x + 2

= 5x2 + 10x + 2

–(x2 – 3x + 12)

= –x2 + 3x – 12

4x2 + 13x – 10

Simplify:

(3x2 – 2x + 8) – (x2 – 4)

3x2 – 2x + 8 + (–x2) + 4

= 2x2 – 2x + 12

(10z2 + 6z + 5) – (z2 – 8z + 7)

10z2 + 6z + 5 + (–z2) + 8z + (–7)

= 9z2 + 14z – 2

Simplify:

3x2 – 7x + 5

7a2 – 2a

– (x2 + 4x + 7)

– (5a2+ 3a)

2x2 – 11x – 2

2a2 – 5a

7x2 – x + 3

4x2 + 3x + 2

– (3x2 – x – 7)

– (2x2 – 3x – 7)

2x2 + 6x + 9

4x2 + 10

Simplify:

2x2 + 5x

3x2 – 2x + 10

– (x2 – 3)

– (2x2+ 4x – 6)

x2 – 6x + 16

x2 + 5x + 3

4x2 – x + 6

3x2 – 5x + 3

– (3x2 – 4)

– (2x2 – x – 4)

x2 – 4x + 7

x2 – x + 10

Simplify:

(4x5+ 3x3 – 3x – 5) – (–2x3 + 3x2 + x + 5)

= 4x5 + 5x3 – 3x2 – 4x – 10

(4d4– 2d2 + 2d + 8) – (5d3 + 7d2 – 3d – 9)

= 4d4 – 5d3 – 9d2 + 5d + 17

(a2+ ab– 3b2) – (b2 + 4a2 – ab)

= –3a2 + 2ab – 4b2

Simplify by finding the perimeter:

x2 + x

c2 + 1

6c + 3

A

B

2x2

2x2

4c2+ 2c + 5

x2 + x

A = 5c2 + 8c + 9

B = 6x2 + 2x

Simplify by finding the perimeter:

2d2 + d – 4

3x2 – 5 x

D

C

3d2– 5d

x2 + 7

3d2– 5d

d2 + 7

D = 9d2 – 9d + 3

C = 8x2 – 10x + 14

Simplify by finding the perimeter:

3x2– 5x

a3 + 2a

a + 1

E

F

x2 + 3

2a3+ a + 3

E = 3a3 + 4a + 4

F = 8x2– 10x + 6