Solve Polynomiallongdivision X^3-6x^2+12x-8 Tiger Algebra Solver

Step 1 :

Equation at the end of step 1 :

Step 2 :

Checking for a perfect cube :

2.1 x3-6x2+12x-8 is not a perfect cube

Trying to factor by pulling out :

2.2 Factoring: x3-6x2+12x-8 Thoughtfully split the expression at hand into groups, each group having two terms :Group 1: x3-8 Group 2: -6x2+12x Pull out from each group separately :Group 1: (x3-8) • (1)Group 2: (x-2) • (-6x)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) = x3-6x2+12x-8Polynomial 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 -8. The factor(s) are: of the Leading Coefficient : 1 of the Trailing Constant : 1 ,2 ,4 ,8 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 x3-6x2+12x-8 can be divided with x-2

Polynomial Long Division :

2.4 Polynomial Long Division Dividing : x3-6x2+12x-8 ("Dividend") By : x-2 ("Divisor")

Quotient : x2-4x+4 Remainder: 0

Trying to factor by splitting the middle term

2.5 Factoring x2-4x+4 The first term is, x2 its coefficient is 1 .The middle term is, -4x its coefficient is -4 .The last term, "the constant", is +4 Step-1 : Multiply the coefficient of the first term by the constant 1 • 4 = 4 Step-2 : Find two factors of 4 whose sum equals the coefficient of the middle term, which is -4 .

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

Multiplying Exponential Expressions :

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

Multiplying Exponential Expressions :

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

Final result :