Holt CA Course 1 12-4Subtracting Polynomials Warm Up Warm Up California Standards California...

Holt CA Course 1

12-4 Subtracting Polynomials

Warm UpWarm UpCalifornia StandardsCalifornia StandardsLesson PresentationLesson Presentation

PreviewPreview

Holt CA Course 1


Warm UpWrite the opposite of each integer.1. 10Subtract.3. 19 – (–12)Add.5. (3x2 + 7) + (x2 – 3x)6. (2m2 – 3m) + (–5m2 + 2)

–10

31 –37

2. –7 7

4. –16 – 21

4x2 – 3x + 7–3m2 – 3m + 2

Holt CA Course 1


Preview of Algebra 1 10.0 Students add, subtract,

multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques.Also covered: 7AF1.3

California Standards

Holt CA Course 1


Recall that to subtract an integer, you add its opposite. To subtract a polynomial, you first need to find its opposite.

Holt CA Course 1


Find the opposite of each polynomial.

Additional Example 1: Finding the Opposite of a Polynomial

A. 8x3y4z2

–(8x3y4z2)–8x3y4z2

The opposite of a positive term is a negative term.

B. –3x4 + 8x2

–(–3x4 + 8x2) 3x4 – 8x2 Distributive Property.

Holt CA Course 1


Find the opposite of the polynomial.

Additional Example 1: Finding the Opposite of a Polynomial

C. 9a6b4 + a4b2 – 1

–(9a6b4 + a4b2 – 1) –9a6b4 – a4b2 + 1 Distributive Property

Holt CA Course 1

12-4 Subtracting PolynomialsCheck It Out! Example 1

Find the opposite of each polynomial.A. 4d2e3f3

–(4d2e3f3)

B. –4a2 + 4a4

–(–4a2 + 4a4) 4a2 – 4a4 Distributive Property

–4d2e3f3

The opposite of a positive term is a negative term.

Holt CA Course 1


Find the opposite of the polynomial.

C. 9a6b4 + a4b2 – 1

–(9a6b4 + a4b2 – 1) –9a6b4 – a4b2 + 1 Distributive Property

Holt CA Course 1


To subtract a polynomial, add its opposite.

Holt CA Course 1


Subtract.

Additional Example 2: Subtracting Polynomials Horizontally

A. (5x2 + 2x – 3) – (3x2 + 8x – 4)

(5x2 + 2x – 3) + (–3x2 – 8x + 4)

5x2 – 3x2 + 2x – 8x – 3 + 4

Add theopposite.CommutativeProperty

2x2 – 6x + 1 Combine liketerms.

Holt CA Course 1


Subtract.

Additional Example 2: Subtracting Polynomials Horizontally

B. (b2 + 4b – 1) – (7b2 – b – 1)

(b2 + 4b – 1) + (–7b2 + b + 1)

b2 – 7b2 + 4b + b – 1 + 1

–6b2 + 5b

Add the opposite.

Commutative Property

Combine like terms.

Holt CA Course 1


Subtract.

A. (2y3 + 3y + 5) – (4y3 + 3y + 5)

Add theopposite.CommutativeProperty

–2y3 Combine liketerms.

(2y3 + 3y + 5) + (–4y3 – 3y – 5)

2y3 – 4y3 + 3y – 3y + 5 – 5

Holt CA Course 1

12-4 Subtracting PolynomialsCheck It Out! Example 2B

Subtract.(c3 + 2c2 + 3) – (4c3 – c2 – 1)

–3c3 + 3c2 + 4

Add the opposite.

Commutative Property

Combine like terms.

(c3 + 2c2 + 3) + (–4c3 + c2 + 1)

c3 – 4c3 + 2c2 + c2 + 3 + 1

Holt CA Course 1


You can also subtract polynomials in a vertical format. Write the second polynomial below the first one, lining up the like terms.

Holt CA Course 1


Subtract.

Additional Example 3: Subtracting Polynomials Vertically

A. (2n2 – 4n + 9) – (6n2 – 7n + 5)

(2n2 – 4n + 9) 2n2 – 4n + 9– (6n2 – 7n + 5) + –6n2 + 7n – 5

–4n2 + 3n + 4Add the opposite.

Holt CA Course 1


Subtract.


B. (10x2 + 2x – 7) – (x2 + 5x + 1)

(10x2 + 2x – 7) 10x2 + 2x – 7– (x2 + 5x + 1) + –x2 – 5x – 1

9x2 – 3x – 8Add the opposite.

Holt CA Course 1


Subtract.


C. (6a4 – 3a2 – 8) – (–2a4 + 7)

(6a4 – 3a2 – 8) 6a4 – 3a2 – 8– (–2a4 + 7) + 2a4 – 7

8a4 – 3a2 – 15 Rearrange terms as needed.

Holt CA Course 1


Subtract.A. (4r3 + 4r + 6) – (6r3 + 3r + 3)

(4r3 + 4r + 6) 4r3 + 4r + 6– (6r3 + 3r + 3) + –6r3 – 3r – 3

–2r3 + r + 3Add the opposite.

Holt CA Course 1


Subtract.B. (13y2 – 2x + 5) – (y2 + 5x – 9)

(13y2 – 2x + 5) 13y2 – 2x + 5– (y2 + 5x – 9) + –y2 – 5x + 9

12y2 – 7x + 14Add the opposite.

Holt CA Course 1


Subtract.C. (5x2 + 2x + 5) – (–3x2 – 7x)

(5x2 + 2x + 5) 5x2 + 2x + 5– (–3x2 – 7x) +3x2 + 7x

8x2 + 9x + 5 Add the opposite.

Holt CA Course 1


Suppose the cost in dollars of producing x bookcases is given by the polynomial 250 + 128x, and the revenue generated from sales is given by the polynomial 216x – 75. Find a polynomial expression for the profit from producing and selling x bookcases, and evaluate the expression for x = 95.

Additional Example 4: Business Application

216x – 75 – (250 + 128x) revenue – cost216x – 75 + (–250 – 128x) Add the opposite.216x – 128x – 75 – 250 Commutative Property88x – 325 Combine like terms.

Holt CA Course 1

12-4 Subtracting PolynomialsAdditional Example 4 Continued

The profit is given by the polynomial 88x – 325.

88(95) – 325 = 8360 – 325 = 8035

The profit is $8035.

For x = 95,

Holt CA Course 1


Suppose the cost in dollars of producing x baseball bats is given by the polynomial 6 + 12x, and the revenue generated from sales is given by the polynomial 35x – 5. Find a polynomial expression for the profit from producing and selling x baseball bats, and evaluate the expression for x = 50.35x – 5 – (6 + 12x) revenue – cost35x – 5 + (–6 – 12x) Add the opposite.35x – 12x – 5 – 6 Commutative Property

23x – 11 Combine like terms.

Holt CA Course 1

12-4 Subtracting PolynomialsCheck It Out! Example 4 Continued

The profit is given by the polynomial 23x – 11.

23(50) – 11 = 1150 – 11 = 1139

The profit is $1139.

For x = 50,

Holt CA Course 1

12-4 Subtracting PolynomialsLesson Quiz

Find the opposite of each polynomial.

Subtract.

3. (3z2 – 7z + 6) – (2z2 + z – 12)

3m3 – 2m2n

z2 – 8z + 18

–3a2b2c3 2. –3m3 + 2m2n

4. –18h3 – (4h3 + h2 – 12h + 2)

5. (3b2c + 5bc2 – 8b2) – (4b2c + 2bc2 – c2)

– b2c + 3bc2 – 8b2 + c2

– 22h3 – h2 + 12h – 2

1. 3a2b2c3

Holt CA Course 1 12-4Subtracting Polynomials Warm Up Warm Up California Standards California...

Documents

Transcript of Holt CA Course 1 12-4Subtracting Polynomials Warm Up Warm Up California Standards California...