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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

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
slide2

9.1 Adding and Subtracting Polynomials

Identify each polynomial by the name and degree

12

monomial constant

8x – 5

binomial linear

4x + 3

binomial linear

x2 + 6

binomial quadratic

3x2 + 6x + 5

trinomial quadratic

x3 + 2x – 2

trinomial cubic

x3 + 4

binomial cubic

slide3

9.1 Adding and Subtracting Polynomials

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

adding polynomials

9.1 Adding and Subtracting Polynomials

Adding Polynomials

in horizontal form:

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

= 4x2 + 3x + 17

in vertical form:

x2 + 2x + 5

+

3x2 + x + 12

= 4x2 + 3x + 17

slide5

9.1 Adding and Subtracting Polynomials

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

slide6

9.1 Adding and Subtracting Polynomials

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

slide7

9.1 Adding and Subtracting Polynomials

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

slide8

9.1 Adding and Subtracting Polynomials

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

slide9

9.1 Adding and Subtracting Polynomials

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

9.1 Adding and Subtracting Polynomials

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

9.1 Adding and Subtracting Polynomials

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

simplify1

9.1 Adding and Subtracting Polynomials

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

simplify2

9.1 Adding and Subtracting Polynomials

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

simplify3

9.1 Adding and Subtracting Polynomials

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

9.1 Adding and Subtracting Polynomials

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 perimeter1

9.1 Adding and Subtracting Polynomials

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 perimeter2

9.1 Adding and Subtracting Polynomials

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