Simplification Or Other Simple Results - Tiger Algebra

Step 1 :

Checking for a perfect cube :

1.1 c3 + c2 - 5c - 5 is not a perfect cube

Trying to factor by pulling out :

1.2 Factoring: c3 + c2 - 5c - 5 Thoughtfully split the expression at hand into groups, each group having two terms :Group 1: -5c - 5 Group 2: c3 + c2 Pull out from each group separately :Group 1: (c + 1) • (-5)Group 2: (c + 1) • (c2) -------------------Add up the two groups : (c + 1) • (c2 - 5) Which is the desired factorization

Trying to factor as a Difference of Squares :

1.3 Factoring: c2 - 5 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 : 5 is not a square !! Ruling : Binomial can not be factored as the difference of two perfect squares.

Trying to factor as a Difference of Squares :

1.4 Factoring: c4 - 25 Check : 25 is the square of 5Check : c4 is the square of c2 Factorization is : (c2 + 5) • (c2 - 5)

Polynomial Roots Calculator :

1.5 Find roots (zeroes) of : F(c) = c2 + 5Polynomial Roots Calculator is a set of methods aimed at finding values of c for which F(c)=0 Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers c 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 5. The factor(s) are: of the Leading Coefficient : 1 of the Trailing Constant : 1 ,5 Let us test ....

Polynomial Roots Calculator found no rational roots

Trying to factor as a Difference of Squares :

1.6 Factoring: c2 - 5 Check : 5 is not a square !! Ruling : Binomial can not be factored as the difference of two perfect squares.

Canceling Out :

1.7 Cancel out (c2 - 5) which appears on both sides of the fraction line.

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 c3 - 2c2 + 5c - 10 is not a perfect cube

Trying to factor by pulling out :

3.2 Factoring: c3 - 2c2 + 5c - 10 Thoughtfully split the expression at hand into groups, each group having two terms :Group 1: 5c - 10 Group 2: c3 - 2c2 Pull out from each group separately :Group 1: (c - 2) • (5)Group 2: (c - 2) • (c2) -------------------Add up the two groups : (c - 2) • (c2 + 5) Which is the desired factorization

Polynomial Roots Calculator :

3.3 Find roots (zeroes) of : F(c) = c2 + 5 See theory in step 1.5 In this case, the Leading Coefficient is 1 and the Trailing Constant is 5. The factor(s) are: of the Leading Coefficient : 1 of the Trailing Constant : 1 ,5 Let us test ....

Polynomial Roots Calculator found no rational roots

Trying to factor by splitting the middle term

3.4 Factoring c2 - c - 2 The first term is, c2 its coefficient is 1 .The middle term is, -c its coefficient is -1 .The last term, "the constant", is -2 Step-1 : Multiply the coefficient of the first term by the constant 1 • -2 = -2 Step-2 : Find two factors of -2 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 1 c2 - 2c + 1c - 2Step-4 : Add up the first 2 terms, pulling out like factors : c • (c-2) Add up the last 2 terms, pulling out common factors : 1 • (c-2) Step-5 : Add up the four terms of step 4 : (c+1) • (c-2) Which is the desired factorization

Canceling Out :

3.5 Cancel out (c-2) which appears on both sides of the fraction line.

Equation at the end of step 3 :

Step 4 :

Canceling Out :

4.1 Cancel out (c2+5) which appears on both sides of the fraction line.

Canceling Out :

4.2 Cancel out (c+1) which appears on both sides of the fraction line.

Final result :