Solve Polynomialrootcalculator X^3-3x^2-3x-1/x-1 Tiger Algebra Solver

Step 1 :

Equation at the end of step 1 :

Step 2 :

Equation at the end of step 2 :

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 :

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 : x3 - 3x2 - 3x = x • (x2 - 3x - 3)

Trying to factor by splitting the middle term

4.2 Factoring x2 - 3x - 3 The first term is, x2 its coefficient is 1 .The middle term is, -3x its coefficient is -3 .The last term, "the constant", is -3 Step-1 : Multiply the coefficient of the first term by the constant 1 • -3 = -3 Step-2 : Find two factors of -3 whose sum equals the coefficient of the middle term, which is -3 .

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

Adding fractions that have a common denominator :

4.3 Adding up the two equivalent fractions Add the two equivalent fractions which now have a common denominatorCombine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

Equation at the end of step 4 :

Step 5 :

Rewriting the whole as an Equivalent Fraction :

5.1 Subtracting a whole from a fraction Rewrite the whole as a fraction using x as the denominator :

Checking for a perfect cube :

5.2 x4 - 3x3 - 3x2 - 1 is not a perfect cube

Trying to factor by pulling out :

5.3 Factoring: x4 - 3x3 - 3x2 - 1 Thoughtfully split the expression at hand into groups, each group having two terms :Group 1: -3x2 - 1 Group 2: -3x3 + x4 Pull out from each group separately :Group 1: (3x2 + 1) • (-1)Group 2: (x - 3) • (x3)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 :

5.4 Find roots (zeroes) of : F(x) = x4 - 3x3 - 3x2 - 1Polynomial 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 integersThe 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 CoefficientIn this case, the Leading Coefficient is 1 and the Trailing Constant is -1. The factor(s) are: of the Leading Coefficient : 1 of the Trailing Constant : 1 Let us test ....

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 p originate from P/Q reduced to its lowest terms In our case this means that x4 - 3x3 - 3x2 - 1 can be divided with x + 1

Polynomial Long Division :

5.5 Polynomial Long Division Dividing : x4 - 3x3 - 3x2 - 1 ("Dividend") By : x + 1 ("Divisor")

Quotient : x3-4x2+x-1 Remainder: 0

Polynomial Roots Calculator :

5.6 Find roots (zeroes) of : F(x) = x3-4x2+x-1 See theory in step 5.4 In this case, the Leading Coefficient is 1 and the Trailing Constant is -1. The factor(s) are: of the Leading Coefficient : 1 of the Trailing Constant : 1 Let us test ....

Polynomial Roots Calculator found no rational roots

Adding fractions that have a common denominator :

5.7 Adding up the two equivalent fractions

Polynomial Roots Calculator :

5.8 Find roots (zeroes) of : F(x) = x4 - 3x3 - 3x2 - x - 1 See theory in step 5.4 In this case, the Leading Coefficient is 1 and the Trailing Constant is -1. The factor(s) are: of the Leading Coefficient : 1 of the Trailing Constant : 1 Let us test ....

Polynomial Roots Calculator found no rational roots

Final result :