Solve Polynomiallongdivision 8x^3-12x^2+6x-1 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 8x3-12x2+6x-1 is not a perfect cube

Trying to factor by pulling out :

3.2 Factoring: 8x3-12x2+6x-1 Thoughtfully split the expression at hand into groups, each group having two terms :Group 1: 6x-1 Group 2: -12x2+8x3 Pull out from each group separately :Group 1: (6x-1) • (1)Group 2: (2x-3) • (4x2)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) = 8x3-12x2+6x-1Polynomial 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 8 and the Trailing Constant is -1. The factor(s) are: of the Leading Coefficient : 1,2 ,4 ,8 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 8x3-12x2+6x-1 can be divided with 2x-1

Polynomial Long Division :

3.4 Polynomial Long Division Dividing : 8x3-12x2+6x-1 ("Dividend") By : 2x-1 ("Divisor")

Quotient : 4x2-4x+1 Remainder: 0

Trying to factor by splitting the middle term

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

Multiplying Exponential Expressions :

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

Multiplying Exponential Expressions :

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

Final result :