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Step 1 :
Equation at the end of step 1 :
Equation at the end of step 2 :
Step 3 :
Checking for a perfect cube :
3.1 8x3 - 10x2 + 9x - 10 is not a perfect cube
Trying to factor by pulling out :
3.2 Factoring: 8x3 - 10x2 + 9x - 10
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 9x - 10
Group 2: -10x2 + 8x3
Pull out from each group separately :
Group 1: (9x - 10) • (1)
Group 2: (4x - 5) • (2x2)
Bad news !! Factoring by pulling out fails :
The groups have no common factor and can not be added up to form a multiplication.
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 9x - 10
Group 2: -10x2 + 8x3
Pull out from each group separately :
Group 1: (9x - 10) • (1)
Group 2: (4x - 5) • (2x2)
Bad news !! Factoring by pulling out fails :
The groups have no common factor and can not be added up to form a multiplication.
Polynomial Roots Calculator :
3.3 Find roots (zeroes) of : F(x) = 8x3 - 10x2 + 9x - 10
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test 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 integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 8 and the Trailing Constant is -10.
The factor(s) are:
of the Leading Coefficient : 1,2 ,4 ,8
of the Trailing Constant : 1 ,2 ,5 ,10
Let us test ..
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test 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 integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 8 and the Trailing Constant is -10.
The factor(s) are:
of the Leading Coefficient : 1,2 ,4 ,8
of the Trailing Constant : 1 ,2 ,5 ,10
Let us test ..
P | Q | P/Q | F(P/Q) | Divisor |
---|---|---|---|---|
-1 | 1 | -1.00 | -37.00 | |
-1 | 2 | -0.50 | -18.00 | |
-1 | 4 | -0.25 | -13.00 | |
-1 | 8 | -0.13 | -11.30 | |
-2 | 1 | -2.00 | -132.00 |
Note - For tidiness, printing of 15 checks which found no root was suppressed
Polynomial Roots Calculator found no rational roots Proencryptor 1 7 7 – professional encryption software.
![Amazing 2 9 8 x 10 shed Amazing 2 9 8 x 10 shed](https://study.com/cimages/videopreview/videopreview-full/u1lcjd1c3e.jpg)
Polynomial Long Division :
8 X 10 Frame
3.4 Polynomial Long Division
Dividing : 8x3 - 10x2 + 9x - 10
('Dividend')
By : 2x - 1 ('Divisor')
Dividing : 8x3 - 10x2 + 9x - 10
('Dividend')
By : 2x - 1 ('Divisor')
dividend | 8x3 | - | 10x2 | + | 9x | - | 10 |
- divisor | * 4x2 | 8x3 | - | 4x2 | |||
remainder | - | 6x2 | + | 9x | - | 10 | |
- divisor | * -3x1 | - | 6x2 | + | 3x | ||
remainder | 6x | - | 10 | ||||
- divisor | * 3x0 | 6x | - | 3 | |||
remainder | - | 7 |
Quotient : 4x2 - 3x + 3
Remainder : -7
Remainder : -7
Final result :
See results of polynomial long division:
1. In step #03.04
More Tips to Remember 8 x 9 = 72
Using Your Fingers
Step 1 Put your hands on the table in front of you. |
Step 2 Your fingers represent the numbers 1 through 10. |
Step 3
|
Fact Navigator
You're learningAmazing 2 9 8 X 10 Shed
9
x8
72
![105 105](https://4.bp.blogspot.com/-ClqFijRE98U/XKEpSWeJfTI/AAAAAAAA3JA/ICi7JObXJMkBdm4qOY-wIANwdKSne6F_ACLcBGAs/s1600/16-Year-Old%2BArtist%2BHas%2BBeen%2BDrawing%2BSince%2BHe%2BWas%2BTwo%2BAnd%2BHere%2BAre%2BHis%2BAmazing%2BIllustrations%2B12.jpg)
8
X 8 64
X 8 64
Amazing 2 9 8 X 105
9
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