Solve Polynomiallongdivision K3-3k2+3k-1 Tiger Algebra Solver

Reformatting the input :

Changes made to your input should not affect the solution: (1): "k2" was replaced by "k^2". 1 more similar replacement(s).

Step 1 :

Equation at the end of step 1 :

Step 2 :

Checking for a perfect cube :

2.1 k3-3k2+3k-1 is not a perfect cube

Trying to factor by pulling out :

2.2 Factoring: k3-3k2+3k-1 Thoughtfully split the expression at hand into groups, each group having two terms :Group 1: 3k-1 Group 2: -3k2+k3 Pull out from each group separately :Group 1: (3k-1) • (1)Group 2: (k-3) • (k2)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(k) = k3-3k2+3k-1Polynomial Roots Calculator is a set of methods aimed at finding values of k for which F(k)=0 Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers k 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 k3-3k2+3k-1 can be divided with k-1

Polynomial Long Division :

2.4 Polynomial Long Division Dividing : k3-3k2+3k-1 ("Dividend") By : k-1 ("Divisor")

Quotient : k2-2k+1 Remainder: 0

Trying to factor by splitting the middle term

2.5 Factoring k2-2k+1 The first term is, k2 its coefficient is 1 .The middle term is, -2k its coefficient is -2 .The last term, "the constant", is +1 Step-1 : Multiply the coefficient of the first term by the constant 1 • 1 = 1 Step-2 : Find two factors of 1 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 -1 k2 - 1k - 1k - 1Step-4 : Add up the first 2 terms, pulling out like factors : k • (k-1) Add up the last 2 terms, pulling out common factors : 1 • (k-1) Step-5 : Add up the four terms of step 4 : (k-1) • (k-1) Which is the desired factorization

Multiplying Exponential Expressions :

2.6 Multiply (k-1) by (k-1) The rule says : To multiply exponential expressions which have the same base, add up their exponents.In our case, the common base is (k-1) and the exponents are : 1 , as (k-1) is the same number as (k-1)1 and 1 , as (k-1) is the same number as (k-1)1 The product is therefore, (k-1)(1+1) = (k-1)2

Multiplying Exponential Expressions :

2.7 Multiply (k-1)2 by (k-1) The rule says : To multiply exponential expressions which have the same base, add up their exponents.In our case, the common base is (k-1) and the exponents are : 2 and 1 , as (k-1) is the same number as (k-1)1 The product is therefore, (k-1)(2+1) = (k-1)3

Final result :