Solve Factoringbinomialsassumordifferenceofcubes X6-2x3-3 Tiger ...

Reformatting the input :

Changes made to your input should not affect the solution: (1): "x3" was replaced by "x^3". 1 more similar replacement(s).

Step 1 :

Equation at the end of step 1 :

Step 2 :

Trying to factor by splitting the middle term

2.1 Factoring x6-2x3-3 The first term is, x6 its coefficient is 1 .The middle term is, -2x3 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, -3 and 1 x6 - 3x3 + 1x3 - 3Step-4 : Add up the first 2 terms, pulling out like factors : x3 • (x3-3) Add up the last 2 terms, pulling out common factors : 1 • (x3-3) Step-5 : Add up the four terms of step 4 : (x3+1) • (x3-3) Which is the desired factorization

Trying to factor as a Sum of Cubes :

2.2 Factoring: x3+1 Theory : A sum of two perfect cubes, a3 + b3 can be factored into : (a+b) • (a2-ab+b2)Proof : (a+b) • (a2-ab+b2) = a3-a2b+ab2+ba2-b2a+b3 = a3+(a2b-ba2)+(ab2-b2a)+b3= a3+0+0+b3= a3+b3Check : 1 is the cube of 1 Check : x3 is the cube of x1Factorization is : (x + 1) • (x2 - x + 1)

Trying to factor by splitting the middle term

2.3 Factoring x2 - x + 1 The first term is, x2 its coefficient is 1 .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 1 • 1 = 1 Step-2 : Find two factors of 1 whose sum equals the coefficient of the middle term, which is -1 .

Observation : No two such factors can be found !! Conclusion : Trinomial can not be factored

Trying to factor as a Difference of Cubes:

2.4 Factoring: x3-3 Theory : A difference of two perfect cubes, a3 - b3 can be factored into (a-b) • (a2 +ab +b2)Proof : (a-b)•(a2+ab+b2) = a3+a2b+ab2-ba2-b2a-b3 = a3+(a2b-ba2)+(ab2-b2a)-b3 = a3+0+0-b3 = a3-b3Check : 3 is not a cube !! Ruling : Binomial can not be factored as the difference of two perfect cubes

Polynomial Roots Calculator :

2.5 Find roots (zeroes) of : F(x) = x3-3Polynomial 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 -3. The factor(s) are: of the Leading Coefficient : 1 of the Trailing Constant : 1 ,3 Let us test ....

Polynomial Roots Calculator found no rational roots

Final result :