Solve Polynomialrootcalculator X^3-5x^2-17x+21 Tiger Algebra Solver

Step 1 :

Equation at the end of step 1 :

Step 2 :

Checking for a perfect cube :

2.1 x3-5x2-17x+21 is not a perfect cube

Trying to factor by pulling out :

2.2 Factoring: x3-5x2-17x+21 Thoughtfully split the expression at hand into groups, each group having two terms :Group 1: -17x+21 Group 2: x3-5x2 Pull out from each group separately :Group 1: (-17x+21) • (1) = (17x-21) • (-1)Group 2: (x-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 :

2.3 Find roots (zeroes) of : F(x) = x3-5x2-17x+21Polynomial 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 21. The factor(s) are: of the Leading Coefficient : 1 of the Trailing Constant : 1 ,3 ,7 ,21 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 x3-5x2-17x+21 can be divided by 3 different polynomials,including by x-7

Polynomial Long Division :

2.4 Polynomial Long Division Dividing : x3-5x2-17x+21 ("Dividend") By : x-7 ("Divisor")

Quotient : x2+2x-3 Remainder: 0

Trying to factor by splitting the middle term

2.5 Factoring x2+2x-3 The first term is, x2 its coefficient is 1 .The middle term is, +2x its coefficient is 2 .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 2 .

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

Final result :