Answers
1 result(s) found
x
3x
3
+x
2
+x−1
See steps
Step by Step Solution:
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STEP
1
:
1
Simplify —
x
Equation at the end of step
1
:
1
(((3 • (x2)) + x) - —) + 1
x
STEP
2
:
Equation at the end of step
2
:
1
((3x2 + x) - —) + 1
x
STEP
3
:
Rewriting the whole as an Equivalent Fraction
3.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using x as the denominator :
3x2 + x (3x2 + x) • x
3x2 + x = ——————— = —————————————
1 x
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
STEP
4
:
Pulling out like terms
4.1 Pull out like factors :
3x2 + x = x • (3x + 1)
Adding fractions that have a common denominator :
4.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
x • (3x+1) • x - (1) 3x3 + x2 - 1
———————————————————— = ————————————
x x
Equation at the end of step
4
:
(3x3 + x2 - 1)
—————————————— + 1
x
STEP
5
:
Rewriting the whole as an Equivalent Fraction
5.1 Adding a whole to a fraction
Rewrite the whole as a fraction using x as the denominator :
1 1 • x
1 = — = —————
1 x
Polynomial Roots Calculator :
5.2 Find roots (zeroes) of : F(x) = 3x3 + x2 - 1
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 3 and the Trailing Constant is -1.
The factor(s) are:
of the Leading Coefficient : 1,3
of the Trailing Constant : 1
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -3.00
-1 3 -0.33 -1.00
1 1 1.00 3.00
1 3 0.33 -0.78
Polynomial Roots Calculator found no rational roots
Adding fractions that have a common denominator :
5.3 Adding up the two equivalent fractions
(3x3+x2-1) + x 3x3 + x2 + x - 1
—————————————— = ————————————————
x x
Checking for a perfect cube :
5.4 3x3 + x2 + x - 1 is not a perfect cube
Trying to factor by pulling out :
5.5 Factoring: 3x3 + x2 + x - 1
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: x - 1
Group 2: 3x3 + x2
Pull out from each group separately :
Group 1: (x - 1) • (1)
Group 2: (3x + 1) • (x2)
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 :
5.6 Find roots (zeroes) of : F(x) = 3x3 + x2 + x - 1
See theory in step 5.2
In this case, the Leading Coefficient is 3 and the Trailing Constant is -1.
The factor(s) are:
of the Leading Coefficient : 1,3
of the Trailing Constant : 1
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -4.00
-1 3 -0.33 -1.33
1 1 1.00 4.00
1 3 0.33 -0.44
Polynomial Roots Calculator found no rational roots
Final result :
3x3 + x2 + x - 1
————————————————
x