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.
9514 1404 393
Answer:
8. 4 +2q²/p² -4r/p +r²/p²
9. (x, y) = (3/4, -17/8)
Step-by-step explanation:
All of these questions are asking you to make use of the fact that ...
α + β = -q/p
αβ = r/p
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8. (2 +α²)(2 +β²) = 4 + 2(α² +β²) +α²β²
= 4 +2((α+β)² -2αβ) +(αβ)²
Substituting the above for the sum and product, you have ...
= 4 + 2((-q/p)² -2(r/p)) +(r/p)²
= 4 +2q²/p² -4r/p +r²/p²
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9. This is asking for the vertex of the parabola. The x-coordinate is ...
x=-b/(2a) = -(-3)/(2(2) = 3/4
Then the y-coordinate is ...
y = (2(3/4) -3)(3/4) -1 = (-3/2)(3/4) -1 = -9/8 -1 = -17/8
The (x, y) values of interest are (3/4, -17/8).
