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Given:
The figure of a triangle DEF.
To find:
The coordinate of image of given triangle after reflection over y-axis.
Solution:
The vertices of given triangle are D(1,4), E(4,3), F(2,0).
If a figure is reflected over the y-axis, then the rule of reflection is
Using this rule, we get
Therefore, the coordinates of image are D'(-1,4), E'(-4,3) and F'(-2,0).
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)