U2 – 2.1 P OLYNOMIALS Naming Polynomials Add and Subtract Polynomials.

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U2 – 2.1 POLYNOMIALS Naming Polynomials Add and Subtract Polynomials

Transcript of U2 – 2.1 P OLYNOMIALS Naming Polynomials Add and Subtract Polynomials.

U2 – 2.1

POLYNOMIALS

Naming PolynomialsAdd and Subtract Polynomials

EXAMPLE 1 Identify polynomial functions

Name each polynomial by degree (highest exponent), the number of terms (and expression that can be written as a sum, the parts added together) leading coefficient (number in front of the variable with highest degree) and type(constant, linier, quadratic, cubic, quartic).

a. 2 + 5

SOLUTION

a. The degree is 4, number of terms is 2, leading coefficient 2, and type is quartic.

EXAMPLE 1 Identify polynomial functions

Name each polynomial by degree, the number of terms, type and leading coefficient.

a. 10a

SOLUTION

a. The degree is 1, the number of terms is 1, type is linear, and the leading coefficient is 10.

EXAMPLE 1 Identify polynomial functions

Name each polynomial by degree, the number of terms, type, leading coefficient

a. - 5 +10n - 2

SOLUTION

a. The degree is 5, the number of terms is 3, type is cubic, and the leading coefficient is 3.

EXAMPLE 1 Identify polynomial functions

Name each polynomial by degree, the number of terms, type and leading coeffcient.

a. 3

SOLUTION

a. The degree is :None and the number of terms is 1, type monomial, leading coefficient none.

GUIDED PRACTICE for Examples 1 and 2

State the polynomials degree, type, terms, and leading coefficient.

1. f (x) = 13 – 2x

SOLUTION

f (x) = – 2x + 13

It is a polynomial function.Standard form: – 2x + 13Degree: 1 Type: linearLeading coefficient of – 2.Number of terms : 2

GUIDED PRACTICE for Examples 1 and 2

2. p (x) = 9x4 – 5x 2 + 4

SOLUTION

It is a polynomial function.Standard form: . p (x) = 9x4 – 5x 2 +

4Degree: 4 Type: quarticLeading coefficient of 9.Number of terms : 4

GUIDED PRACTICE for Examples 1 and 2

3. h (x) = 6x2 + π – 3x

SOLUTION

h (x) = 6x2 – 3x + π

The function is a polynomial function that is already written in standard form will be 6x2– 3x + π .

It has degree 2 (quadratic) and a leading coefficient of 6.

It is a polynomial function.Standard form: 6– 3x + π Degree: 2 Type: quadraticTerms: 3Leading coefficient of 6

EXAMPLE 1 Add polynomials vertically and horizontally

a. Add 2x3 – 5x2 + 3x – 9 and x3 + 6x2 + 11 in a vertical format.

SOLUTION

a. 2x3 – 5x2 + 3x – 9

+ x3 + 6x2 + 11

3x3 + x2 + 3x + 2

EXAMPLE 1 Add polynomials vertically and horizontally

(3y3 – 2y2 – 7y) + (– 4y2 + 2y – 5)

= 3y3 – 2y2 – 4y2 – 7y + 2y – 5

= 3y3 – 6y2 – 5y – 5

b. Add 3y3 – 2y2 – 7y and – 4y2 + 2y – 5 in a horizontal format.

EXAMPLE 2 Subtract polynomials vertically and horizontally

a. Subtract 3x3 + 2x2 – x + 7 from 8x3 – x2 – 5x + 1 in a vertical format.

SOLUTION

a. Align like terms, then add the opposite of the subtracted polynomial.

8x3 – x2 – 5x + 1

– (3x3 + 2x2 – x + 7)

8x3 – x2 – 5x + 1

+ – 3x3 – 2x2 + x – 7

5x3 – 3x2 – 4x – 6

EXAMPLE 2

Write the opposite of the subtracted polynomial, then add like terms.

(4z2 + 9z – 12) – (5z2 – z + 3) = 4z2 + 9z – 12 – 5z2 + z – 3

= 4z2 – 5z2 + 9z + z – 12 – 3

= – z2 + 10z – 15

Subtract polynomials vertically and horizontally

b. Subtract 5z2 – z + 3 from 4z2 + 9z – 12 in a horizontal format.

GUIDED PRACTICE for Examples 1 and 2

Find the sum or difference.

1. (t2 – 6t + 2) + (5t2 – t – 8)

SOLUTION

6t2 – 7t – 6

t2 – 6t + 2

+ 5t2 – t – 8

GUIDED PRACTICE for Examples 1 and 2

2. (8d – 3 + 9d3) – (d3 – 13d2 – 4)

SOLUTION

= (8d – 3 + 9d3) – (d3 – 13d2 – 4)

= (8d – 3 + 9d3) – d3 + 13d2 + 4)

= 9d3 –3 d3 + 13d2 + 8d – 3 + 4

= 8d3 + 13d2 + 8d + 1

TRY THE FOLLOWING PROBLEMSVertical or Horizontal

1. ( 3 - 5 ) + ( 7 - 3 )

2. ( 5 + 7c + 3 ) + ( + 6c + 4 )

3. ( - 3 - 2x + 2) + ( + 6 + 4 )

ANSWERS TO ADDITION PROBLEMS

1. ( 3 - 5 ) + ( 7 - 3 ) = 10 - 8

2. ( 5 + 7c + 3 ) + ( + 6c + 4 ) = 6 + 13c + 7

3. ( - 3 - 2x + 2) + ( + 6 + 4 ) = 11 -2x + 6

TRY THE FOLLOWING PROBLEMSVertical or Horizontal

1. ( 4 - 9 ) - ( 2 - 3 )

2. ( 4 + 2c + 6 ) - ( + 8c + 4 )

3. ( - 8 - 3x + 9 ) - ( - + 4 + 5 )

ANSWERS TO THE SUBTRACT PROBLEMS

1. ( 4 - 9 ) - ( 2 - 3 ) = - 6

2. ( 4 + 2c + 6 ) - ( + 8c + 4 ) = 3

3. ( - 8 - 3x + 9 ) - ( - + 4 + 5 )

= -3x + 4