Indicate whether each system of equations has no solution, one solution, or infinitely many solutions. y=2x+2y=2x+4
1 answer:
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Answer:
Correct factorization: (x+2)(x+3)(x-3)
Step-by-step explanation:
The given 4 term polynomial is:
Part a) Jay's Mistake:
Factorization of Jay was:
Though this expression will simplify to original given expression but this is not the complete and final factorization. The second factor which is x² - 9 can be factored further, which is shown in the next part.
Part b) Complete Factorization
In order to factor a 4 term expression of the type given in the question, the first step is to take the common from similar terms. You might need to re-arrange the terms before taking common in some case. Taking commons from the given expression, we get:
Jay stopped at this step. At this step you need to look if any part of the expression can be factored further. Luckily, in this case x² - 9 can be factored further as its a difference of perfect squares:
x² - 9 = x² - (3)² = (x + 3)(x - 3)
Using these factors of x² - 9 in previous expression, we get:
This is the final factored form of the given 4 term expression as it can not be factored further in any way.