Other Factorizations - Tiger Algebra

Reformatting the input :

Changes made to your input should not affect the solution: (1): "m3" was replaced by "m^3". 1 more similar replacement(s).

Step 1 :

Step 2 :

Pulling out like terms :

2.1 Pull out like factors : m5 + m3 - 6m = m • (m4 + m2 - 6)

Trying to factor by splitting the middle term

2.2 Factoring m4 + m2 - 6 The first term is, m4 its coefficient is 1 .The middle term is, +m2 its coefficient is 1 .The last term, "the constant", is -6 Step-1 : Multiply the coefficient of the first term by the constant 1 • -6 = -6 Step-2 : Find two factors of -6 whose sum equals the coefficient of the middle term, which is 1 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and 3 m4 - 2m2 + 3m2 - 6Step-4 : Add up the first 2 terms, pulling out like factors : m2 • (m2-2) Add up the last 2 terms, pulling out common factors : 3 • (m2-2) Step-5 : Add up the four terms of step 4 : (m2+3) • (m2-2) Which is the desired factorization

Polynomial Roots Calculator :

2.3 Find roots (zeroes) of : F(m) = m2+3Polynomial Roots Calculator is a set of methods aimed at finding values of m for which F(m)=0 Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers m 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

Trying to factor as a Difference of Squares :

2.4 Factoring: m2-2 Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)Proof : (A+B) • (A-B) = A2 - AB + BA - B2 = A2 - AB + AB - B2 = A2 - B2Note : AB = BA is the commutative property of multiplication. Note : - AB + AB equals zero and is therefore eliminated from the expression.Check : 2 is not a square !! Ruling : Binomial can not be factored as the difference of two perfect squares.

Final result :