Answer:
9x3 + 12x2 - 3x - 11
————————————————————
3x + 1
Step-by-step explanation:STEP
1
:
Equation at the end of step
1
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STEP
2
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Equation at the end of step
2
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STEP
3
:
9x3 + 12x2 - 3x - 11
Simplify ————————————————————
3x + 1
Checking for a perfect cube :
3.1 9x3 + 12x2 - 3x - 11 is not a perfect cube
Trying to factor by pulling out :
3.2 Factoring: 9x3 + 12x2 - 3x - 11
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: -3x - 11
Group 2: 9x3 + 12x2
Pull out from each group separately :
Group 1: (3x + 11) • (-1)
Group 2: (3x + 4) • (3x2)
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) = 9x3 + 12x2 - 3x - 11
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 9 and the Trailing Constant is -11.
The factor(s) are:
of the Leading Coefficient : 1,3 ,9
of the Trailing Constant : 1 ,11
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -5.00
-1 3 -0.33 -9.00
-1 9 -0.11 -10.53
-11 1 -11.00 -10505.00
-11 3 -3.67 -282.33
-11 9 -1.22 -5.84
1 1 1.00 7.00
1 3 0.33 -10.33
1 9 0.11 -11.17
11 1 11.00 13387.00
11 3 3.67 583.00
11 9 1.22 19.69
Polynomial Roots Calculator found no rational roots
Polynomial Long Division :
3.4 Polynomial Long Division
Dividing : 9x3 + 12x2 - 3x - 11
("Dividend")
By : 3x + 1 ("Divisor")
dividend 9x3 + 12x2 - 3x - 11
- divisor * 3x2 9x3 + 3x2
remainder 9x2 - 3x - 11
- divisor * 3x1 9x2 + 3x
remainder - 6x - 11
- divisor * -2x0 - 6x - 2
remainder - 9
Quotient : 3x2 + 3x - 2
Remainder : -9
Final result :
9x3 + 12x2 - 3x - 11
————————————————————
3x + 1
