Exercise
Factor the polynomial equation
Final Answer
Solution
First solution:
To reach a quadratic equation, we define a new variable:
We set the new variable:
We got a quadratic equation. Our equation coefficients are
We solve it with the quadratic formula. Putting the coefficients in the formula gives us
Hence, we get the solutions:
Thus, the factorizing of the quadratic equation is
Going back to the original variable we get
We break down the first factor using Short Multiplication Formulas (third formula) and get the factorizing
Second solution:
We express the second expression as sum and we get
We extract a common factor from the first two expressions:
Once again we extract a common factor – this time the expression in parentheses:
We break down the first factor using Short Multiplication Formulas (third formula) and get the factorizing:
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