Solve Polynomialrootcalculator X3-4x2-3x-10 Tiger Algebra Solver

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Reformatting the input :

Changes made to your input should not affect the solution: (1): "x2" was replaced by "x^2". 1 more similar replacement(s).

Step 1 :

Equation at the end of step 1 :

(((x3) - 22x2) - 3x) - 10

Step 2 :

Checking for a perfect cube :

2.1 x3-4x2-3x-10 is not a perfect cube

Trying to factor by pulling out :

2.2 Factoring: x3-4x2-3x-10 Thoughtfully split the expression at hand into groups, each group having two terms :Group 1: -3x-10 Group 2: x3-4x2 Pull out from each group separately :Group 1: (3x+10) • (-1)Group 2: (x-4) • (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 :

2.3 Find roots (zeroes) of : F(x) = x3-4x2-3x-10Polynomial 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 -10. The factor(s) are: of the Leading Coefficient : 1 of the Trailing Constant : 1 ,2 ,5 ,10 Let us test ....

PQP/QF(P/Q)Divisor
-1 1 -1.00 -12.00
-2 1 -2.00 -28.00
-5 1 -5.00 -220.00
-10 1 -10.00 -1380.00
1 1 1.00 -16.00
2 1 2.00 -24.00
5 1 5.00 0.00 x-5
10 1 10.00 560.00

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 x3-4x2-3x-10 can be divided with x-5

Polynomial Long Division :

2.4 Polynomial Long Division Dividing : x3-4x2-3x-10 ("Dividend") By : x-5 ("Divisor")

dividend x3 - 4x2 - 3x - 10
- divisor * x2 x3 - 5x2
remainder x2 - 3x - 10
- divisor * x1 x2 - 5x
remainder 2x - 10
- divisor * 2x0 2x - 10
remainder0

Quotient : x2+x+2 Remainder: 0

Trying to factor by splitting the middle term

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

-2 + -1 = -3
-1 + -2 = -3
1 + 2 = 3
2 + 1 = 3

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

Final result :

(x2 + x + 2) • (x - 5)

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