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![10.5 10.5](https://i1.wp.com/ramenswag.com/wp-content/uploads/2016/06/tsunade9NanaRamp.jpg?resize=642%2C1041)
Step 1 :
Equation at the end of step 1 :
Equation at the end of step 2 :
Step 3 :
Checking for 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
Polynomial Long Division :
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 |
Amazing 2 9 8 X 105
Quotient : 4x2 - 3x + 3
Remainder : -7
Remainder : -7
Final result :
![Amazing Amazing](https://cdn1.byjus.com/wp-content/uploads/2019/11/RD-Sharma-Solutions-for-Class-10-Chapter-8-Quadratic-Equations-33.jpg)
Amazing 2 9 8 X 10.5
See results of polynomial long division:1. In step #03.04