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McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
Study Guide and Review
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Exercise 64 Page 83

Divide the area by the length to find the width.

w=3x+7 units

Practice makes perfect

To find the missing side length of this rectangle we will need to factor. The area is a trinomial, 6x^2+11x-7. We can solve by factoring the trinomial where a=6, b=11, and c = -7. We need to find two factors of ac=-42 that have a sum of b.

Factors of -42 Sum of factors
-1 and 42 41
-2 and 21 19
-3 and 14 11
Since -3 and 14 are the values we seek, let's split our linear term into 11x=-3x + 14x then factor.
6x^2+11x-7
â–Ľ
Factor
Substitute

11x= -3x + 14x

6x^2 -3x + 14x-7
FactorOut

Factor out 3x

3x(2x-1) + 14x-7
FactorOut

Factor out 7

3x(2x-1) + 7(2x-1)
FactorOut

Factor out 2x-1

(3x+7)(2x-1)

Since we already have the length l=2x-1, the other factor must be the width. w=3x+7

Alternative Solution

 Using 2x-1
The area is a trinomial, 6x^2+11x-7 and width is a binomial, 2x-1. Essentially, we need to find a missing factor, ax+b to multiply by 2x-1 to get 6x^2+11x-7. & 6x^2+ 11x+(-7) &= (2x-1)(ax + b) &= 2ax^2+( 2b-a)x+(-b) In this scenario, 6 = 2a and - 7= - b. Let's solve for a and b.
lc6 =2a & (I) - 7= - b & (II)
DivEqn

(I): .LHS /2.=.RHS /2.

l3 = a - 7= - b
DivEqn

(II): .LHS /(- 1).=.RHS /(- 1).

l3 = a 7= b

(I), (II):Rearrange equation

la=3 b=7
Now, we can say the second factor representing the width of the rectangle is 3x+7.
Subchapter links expand_more
arrow_right 1 Adding and Subtracting Polynomials p.81
11
Adding and Subtracting Polynomials 12 (Page 81)
Adding and Subtracting Polynomials 13 (Page 81)
Adding and Subtracting Polynomials 14 (Page 81)
Adding and Subtracting Polynomials 15 (Page 81)
Adding and Subtracting Polynomials 16 (Page 81)
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Adding and Subtracting Polynomials 18 (Page 81)
arrow_right 2 Multiplying a Polynomial by a Monomial p.81
Multiplying a Polynomial by a Monomial 19 (Page 81)
Multiplying a Polynomial by a Monomial 20 (Page 81)
Multiplying a Polynomial by a Monomial 21 (Page 81)
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arrow_right 3 Multiplying Polynomials p.81
Multiplying Polynomials 23 (Page 81)
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Multiplying Polynomials 26 (Page 81)
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arrow_right 4 Special Products p.82
Special Products 28 (Page 82)
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arrow_right 5 Using the Distributive Property p.82
Using the Distributive Property 35 (Page 82)
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arrow_right 6 Solving x^2+bx+c=0 p.83
Solving x^2+bx+c=0 46 (Page 83)
Solving x^2+bx+c=0 47 (Page 83)
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Solving x^2+bx+c=0 49 (Page 83)
Solving x^2+bx+c=0 50 (Page 83)
Solving x^2+bx+c=0 51 (Page 83)
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arrow_right 7 Solving ax^2+bx+c=0 p.83
Solving ax^2+bx+c=0 56 (Page 83)
Solving ax^2+bx+c=0 57 (Page 83)
Solving ax^2+bx+c=0 58 (Page 83)
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arrow_right 8 Differences of Squares p.84
Differences of Squares 65 (Page 84)
Differences of Squares 66 (Page 84)
Differences of Squares 67 (Page 84)
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arrow_right 9 Perfect Squares p.84
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arrow_right 10 Roots and Zeros p.85
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