# The Lumber Estimator: Board And Surface Measure Contents Of Fractional Sizes

### x(x-1)(x-2)(x-3)-24

This solution đơn hàng with finding the roots (zeroes) of polynomials.

Bạn đang xem: The lumber estimator: board and surface measure contents of fractional sizes

## Step by Step Solution

## Step 1 :

Equation at the end of step 1 : ((x • (x - 1) • (x - 2)) • (x - 3)) - 24## Step 2 :

Equation at the kết thúc of step 2 : (x • (x - 1) • (x - 2) • (x - 3)) - 24## Step 3 :

Equation at the over of step 3 : x • (x - 1) • (x - 2) • (x - 3) - 24## Step 4 :

### Polynomial Roots Calculator :

4.1 Find roots (zeroes) of : F(x) = x4-6x3+11x2-6x-24Polynomial Roots Calculator is a mix of methods aimed at finding values ofxfor which F(x)=0 Rational Roots demo is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integersThe Rational Root Theorem states that if a polynomial zeroes for a rational numberP/Q then phường is a factor of the Trailing Constant và Q is a factor of the Leading CoefficientIn this case, the Leading Coefficient is 1 và the Trailing Constant is -24. The factor(s) are: of the Leading Coefficient : 1of the Trailing Constant : 1 ,2 ,3 ,4 ,6 ,8 ,12 ,24 Let us test ....Xem thêm: Hướng Dẫn Cách Nấu Lẩu Gà Ăn Với Rau Gì ? Lẩu Gà Ăn Với Rau Gì

PQP/QF(P/Q)Divisor

-1 | 1 | -1.00 | 0.00 | x+1 | |||||

-2 | 1 | -2.00 | 96.00 | ||||||

-3 | 1 | -3.00 | 336.00 | ||||||

-4 | 1 | -4.00 | 816.00 | ||||||

-6 | 1 | -6.00 | 3000.00 | ||||||

-8 | 1 | -8.00 | 7896.00 | ||||||

-12 | 1 | -12.00 | 32736.00 | ||||||

-24 | 1 | -24.00 | 421176.00 | ||||||

1 | 1 | 1.00 | -24.00 | ||||||

2 | 1 | 2.00 | -24.00 | ||||||

3 | 1 | 3.00 | -24.00 | ||||||

4 | 1 | 4.00 | 0.00 | x-4 | |||||

6 | 1 | 6.00 | 336.00 | ||||||

8 | 1 | 8.00 | 1656.00 | ||||||

12 | 1 | 12.00 | 11856.00 | ||||||

24 | 1 | 24.00 | 255000.00 |

The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p note that q and phường originate from P/Q reduced khổng lồ its lowest terms In our case this means that x4-6x3+11x2-6x-24can be divided by 2 different polynomials,including by x-4

### Polynomial Long Division :

4.2 Polynomial Long Division Dividing : x4-6x3+11x2-6x-24("Dividend") By:x-4("Divisor")

dividend | x4 | - | 6x3 | + | 11x2 | - | 6x | - | 24 | ||

-divisor | * x3 | x4 | - | 4x3 | |||||||

remainder | - | 2x3 | + | 11x2 | - | 6x | - | 24 | |||

-divisor | * -2x2 | - | 2x3 | + | 8x2 | ||||||

remainder | 3x2 | - | 6x | - | 24 | ||||||

-divisor | * 3x1 | 3x2 | - | 12x | |||||||

remainder | 6x | - | 24 | ||||||||

-divisor | * 6x0 | 6x | - | 24 | |||||||

remainder | 0 |

Quotient : x3-2x2+3x+6 Remainder: 0

### Polynomial Roots Calculator :

4.3 Find roots (zeroes) of : F(x) = x3-2x2+3x+6See theory in step 4.1 In this case, the Leading Coefficient is 1 and the Trailing Constant is 6. The factor(s) are: of the Leading Coefficient : 1of the Trailing Constant : 1 ,2 ,3 ,6 Let us kiểm tra ....

Xem thêm: 【Cảnh Báo】 1 Tuần Nên Tẩy Tế Bào Chết Body Mấy Lần 1 Tuần, &Ndash Dhc Việt Nam

-1 | 1 | -1.00 | 0.00 | x+1 | |||||

-2 | 1 | -2.00 | -16.00 | ||||||

-3 | 1 | -3.00 | -48.00 | ||||||

-6 | 1 | -6.00 | -300.00 | ||||||

1 | 1 | 1.00 | 8.00 | ||||||

2 | 1 | 2.00 | 12.00 | ||||||

3 | 1 | 3.00 | 24.00 | ||||||

6 | 1 | 6.00 | 168.00 |

The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p cảnh báo that q and phường originate from P/Q reduced to lớn its lowest terms In our case this means that x3-2x2+3x+6can be divided with x+1

### Polynomial Long Division :

4.4 Polynomial Long Division Dividing : x3-2x2+3x+6("Dividend") By:x+1("Divisor")

dividend | x3 | - | 2x2 | + | 3x | + | 6 | ||

-divisor | * x2 | x3 | + | x2 | |||||

remainder | - | 3x2 | + | 3x | + | 6 | |||

-divisor | * -3x1 | - | 3x2 | - | 3x | ||||

remainder | 6x | + | 6 | ||||||

-divisor | * 6x0 | 6x | + | 6 | |||||

remainder | 0 |

Quotient : x2-3x+6 Remainder: 0

Trying to lớn factor by splitting the middle term4.5Factoring x2-3x+6 The first term is, x2 its coefficient is 1.The middle term is, -3x its coefficient is -3.The last term, "the constant", is +6Step-1 : Multiply the coefficient of the first term by the constant 1•6=6Step-2 : Find two factors of 6 whose sum equals the coefficient of the middle term, which is -3.

-6 | + | -1 | = | -7 | ||

-3 | + | -2 | = | -5 | ||

-2 | + | -3 | = | -5 | ||

-1 | + | -6 | = | -7 | ||

1 | + | 6 | = | 7 | ||

2 | + | 3 | = | 5 | ||

3 | + | 2 | = | 5 | ||

6 | + | 1 | = | 7 |

Observation : No two such factors can be found !! Conclusion : Trinomial can not be factored