For Problems , find all real number solutions for each equation. (Objective 3)
All the real number solutions for the given problem.
i) The Difference of Two Squares pattern is .
ii) Multiplication is commutative, so the order of writing the factors is not important. For example, can also be written as .
iii) if and only if or .
The following steps have been followed to find out the solutions:
Step-1: Set the polynomial equal to zero.
Step-2: Find out the common monomial factor and rewrite the equation.
Step-3: Convert the equation from step-2 in the form of 2 squares with subtraction and compare with the difference of two squares pattern.
Step-4: Apply the difference of two squares pattern to the equation available in the step-3.
Step-5: Solve the equations from step-2 and step-4, and write the solutions set.
1) The given polynomial is .
Set the above polynomial as an equation by equate with zero.
That is, .
2) The common monomial factor available in the above equation is .
So, the equation can be written as, .
Therefore, or .
3) The above equation can be written as,
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