Solve Polynomialrootcalculator 2x3-3x2-5x+6 Tiger Algebra Solver

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 :

Step 2 :

Equation at the end of step 2 :

Step 3 :

Checking for a perfect cube :

3.1 2x3-3x2-5x+6 is not a perfect cube

Trying to factor by pulling out :

3.2 Factoring: 2x3-3x2-5x+6 Thoughtfully split the expression at hand into groups, each group having two terms :Group 1: -5x+6 Group 2: 2x3-3x2 Pull out from each group separately :Group 1: (-5x+6) • (1) = (5x-6) • (-1)Group 2: (2x-3) • (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 :

3.3 Find roots (zeroes) of : F(x) = 2x3-3x2-5x+6Polynomial 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 2 and the Trailing Constant is 6. The factor(s) are: of the Leading Coefficient : 1,2 of the Trailing Constant : 1 ,2 ,3 ,6 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 2x3-3x2-5x+6 can be divided by 3 different polynomials,including by x-2

Polynomial Long Division :

3.4 Polynomial Long Division Dividing : 2x3-3x2-5x+6 ("Dividend") By : x-2 ("Divisor")

Quotient : 2x2+x-3 Remainder: 0

Trying to factor by splitting the middle term

3.5 Factoring 2x2+x-3 The first term is, 2x2 its coefficient is 2 .The middle term is, +x its coefficient is 1 .The last term, "the constant", is -3 Step-1 : Multiply the coefficient of the first term by the constant 2 • -3 = -6 Step-2 : Find two factors of -6 whose sum equals the coefficient of the middle term, which is 1 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and 3 2x2 - 2x + 3x - 3Step-4 : Add up the first 2 terms, pulling out like factors : 2x • (x-1) Add up the last 2 terms, pulling out common factors : 3 • (x-1) Step-5 : Add up the four terms of step 4 : (2x+3) • (x-1) Which is the desired factorization

Final result :