Answer:
The position and orientation of the new angle may vary, but it should have the same angle measure as ∠BAC
.Step-by-step explanation:
Factor the trinomial below.4x2 + 12x +9
1 answer:
The factor of the trinomial is
Explanation:
The given trinomial is
We need to determine the factor of the trinomial.
The factor of the trinomial can be determined by finding the root of the trinomial.
Let us factorize the trinomial
Thus, the trinomial can be written as,
Grouping the terms, we have,
Simplifying the terms, we get,
Multiplying the terms, we have,
Thus, the factor of the trinomial is
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Answer:
- x = ±√3, and they are actual solutions
- x = 3, but it is an extraneous solution
Step-by-step explanation:
The method often recommended for solving an equation of this sort is to multiply by the product of the denominators, then solve the resulting polynomial equation. When you do that, you get ...
... x^2(6x -18) = (2x -6)(9)
... 6x^2(x -3) -18(x -3) = 0
...6(x -3)(x^2 -3) = 0
... x = 3, x = ±√3
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Alternatively, you can subtract the right side of the equation and collect terms to get ...
... x^2/(2(x -3)) - 9/(6(x -3)) = 0
... (1/2)(x^2 -3)/(x -3) = 0
Here, the solution will be values of x that make the numerator zero:
... x = ±√3
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So, the actual solutions are x = ±3, and x = 3 is an extraneous solution. The value x=3 is actually excluded from the domain of the original equation, because the equation is undefined at that point.
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<em>Comment on the graph</em>
For the graph, we have rewritten the equation so it is of the form f(x)=0. The graphing program is able to highlight zero crossings, so this is a convenient form. When the equation is multiplied as described above, the resulting cubic has an extra zero-crossing at x=3 (blue curve). This is the extraneous solution.
