Solve Polynomialrootcalculator 2x^3-5x^2+x+2 Tiger Algebra Solver

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

Trying to factor by pulling out :

3.2 Factoring: 2x3-5x2+x+2 Thoughtfully split the expression at hand into groups, each group having two terms :Group 1: x+2 Group 2: 2x3-5x2 Pull out from each group separately :Group 1: (x+2) • (1)Group 2: (2x-5) • (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) = 2x3-5x2+x+2Polynomial 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 2. The factor(s) are: of the Leading Coefficient : 1,2 of the Trailing Constant : 1 ,2 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 2x3-5x2+x+2 can be divided by 3 different polynomials,including by x-2

Polynomial Long Division :

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

Quotient : 2x2-x-1 Remainder: 0

Trying to factor by splitting the middle term

3.5 Factoring 2x2-x-1 The first term is, 2x2 its coefficient is 2 .The middle term is, -x its coefficient is -1 .The last term, "the constant", is -1 Step-1 : Multiply the coefficient of the first term by the constant 2 • -1 = -2 Step-2 : Find two factors of -2 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 1 2x2 - 2x + 1x - 1Step-4 : Add up the first 2 terms, pulling out like factors : 2x • (x-1) Add up the last 2 terms, pulling out common factors : 1 • (x-1) Step-5 : Add up the four terms of step 4 : (2x+1) • (x-1) Which is the desired factorization

Final result :