Solve Otherfactorizations X3-4x2-7x+28=0 Tiger Algebra Solver

Reformatting the input :

Changes made to your input should not affect the solution: (1): "x2" was replaced by "x^2". 1 more similar replacement(s).

Step by step solution :

Step 1 :

Equation at the end of step 1 :

Step 2 :

Checking for a perfect cube :

2.1 x3-4x2-7x+28 is not a perfect cube

Trying to factor by pulling out :

2.2 Factoring: x3-4x2-7x+28 Thoughtfully split the expression at hand into groups, each group having two terms :Group 1: -7x+28 Group 2: -4x2+x3 Pull out from each group separately :Group 1: (x-4) • (-7)Group 2: (x-4) • (x2) -------------------Add up the two groups : (x-4) • (x2-7) Which is the desired factorization

Trying to factor as a Difference of Squares :

2.3 Factoring: x2-7 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 : 7 is not a square !! Ruling : Binomial can not be factored as the difference of two perfect squares.

Equation at the end of step 2 :

Step 3 :

Theory - Roots of a product :

3.1 A product of several terms equals zero.When a product of two or more terms equals zero, then at least one of the terms must be zero.We shall now solve each term = 0 separatelyIn other words, we are going to solve as many equations as there are terms in the productAny solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

3.2 Solve : x2-7 = 0Add 7 to both sides of the equation : x2 = 7 When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get: x = ± √ 7 The equation has two real solutions These solutions are x = ± √7 = ± 2.6458

Solving a Single Variable Equation :

3.3 Solve : x-4 = 0Add 4 to both sides of the equation : x = 4

Three solutions were found :

1. x = 4
2. x = ± √7 = ± 2.6458