Answer: (x + 2)(3x - 2)(2x + 1)
<u>Step-by-step explanation:</u>
First, find the possible rational roots. Then use synthetic division (or long division) to find a root. Next, factor the reduced polynomial.
6x³ + 11x² - 4x - 4
P = 4: ± <u>1, 2, 4</u>
Q = 6: ± 1, 2, 3
Possible rational roots are: ± {1, 2, 4, 
}
Try x = -2 --> <em>which is the factor (x + 2)</em>
-2 | 6 11 -4 -4
|<u> ↓ -12 2 4 </u>
6 -1 -2 0 ← Remainder of 0 means (x + 2) is a factor
The reduced polynomial is:
6x² - 1x - 2
Factors of (6)(-2) = -12
∧
1 -12 = -11
2 -6 = -4
3 -4 = -1 this works!
Replace -1x with +3x - 4x and use the grouping method to factor:
6x² + 3x -4x -2
3x<u>(2x + 1)</u> -2<u>(2x + 1)</u> So the factors are: (3x - 2) and (2x + 1)
Since angles XYZ and RYS are vertical angles, they must have the same measure. Consequently,
From there, solve for x:
An exponent is customarily indcated using a caret (^), the character above the "6" on most keyboards. People like to write your first term as sin^2(x), but it is perhaps better written as sin(x)^2, the square of sin(x). Note that parentheses are required to identify the argument of the sine function.
You can let some variable stand for sin(x), such as ...
.. z = sin(x)
Now, the expression can be written as
.. z^2 +z -2
This quadratic expression can be factored in the usual way: find two factors of -2 (the constant term) that add to +1 (the coefficient of z).
You know
.. -2 = -1*2 = -2*1
The first factor pair (-1, 2) sums to +1, so we can write the factorization as
.. z^2 +z -2 = (z -1)(z +2)
In terms of the trig function, this is
.. sin(x)^2 +sin(x) -2 = (sin(x) -1)*(sin(x) +2)
Hi,
When doing the math, 7.864 × 3.290 = 25.872. I'm not exactly sure how you got the numbers 24 or 32.
Hope this helps!
