Holt CA Course 1 12-4Subtracting Polynomials Warm Up Warm Up California Standards California...
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Transcript of 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
12-4 Subtracting Polynomials
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
12-4 Subtracting Polynomials
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
12-4 Subtracting Polynomials
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
12-4 Subtracting Polynomials
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
12-4 Subtracting Polynomials
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
12-4 Subtracting PolynomialsCheck It Out! Example 1
Find the opposite of the polynomial.
C. 9a6b4 + a4b2 – 1
–(9a6b4 + a4b2 – 1) –9a6b4 – a4b2 + 1 Distributive Property
Holt CA Course 1
12-4 Subtracting Polynomials
To subtract a polynomial, add its opposite.
Holt CA Course 1
12-4 Subtracting Polynomials
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
12-4 Subtracting Polynomials
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
12-4 Subtracting PolynomialsCheck It Out! Example 2
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
12-4 Subtracting Polynomials
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
12-4 Subtracting Polynomials
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
12-4 Subtracting Polynomials
Subtract.
Additional Example 3: Subtracting Polynomials Vertically
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
12-4 Subtracting Polynomials
Subtract.
Additional Example 3: Subtracting Polynomials Vertically
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
12-4 Subtracting PolynomialsCheck It Out! Example 3
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
12-4 Subtracting PolynomialsCheck It Out! Example 3
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
12-4 Subtracting PolynomialsCheck It Out! Example 3
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
12-4 Subtracting Polynomials
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
12-4 Subtracting PolynomialsCheck It Out! Example 4
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