This is how you solve the problem
The correct option about the proof is C. Both Amanda and Stephen are correct.
<h3>How to illustrate the information?</h3>
It should be noted that both Amanda and Stephan are correct as they are taking two different pairs of supplementary angles.
Amanda's proof is that he takes (∠1 and ∠4) and (∠3 and ∠4)as the supplementary angles and writes ∠1 + ∠4 = 180° and ∠3 + ∠4 = 180°,
Stephan's proof is that he takes (∠1 and ∠2) and (∠3 and ∠4) as the <em>supplementary</em> angle pair.
Therefore, the correct option is C.
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D. 32/47
You would subtract 1580 from 640 to get 940. You would then simplify 640/940 to get 32/47.
If <em>x</em> + 1 is a factor of <em>p(x)</em> = <em>x</em>³ + <em>k</em> <em>x</em>² + <em>x</em> + 6, then by the remainder theorem, we have
<em>p</em> (-1) = (-1)³ + <em>k</em> (-1)² + (-1) + 6 = 0 → <em>k</em> = -4
So we have
<em>p(x)</em> = <em>x</em>³ - 4<em>x</em>² + <em>x</em> + 6
Dividing <em>p(x)</em> by <em>x</em> + 1 (using whatever method you prefer) gives
<em>p(x)</em> / (<em>x</em> + 1) = <em>x</em>² - 5<em>x</em> + 6
Synthetic division, for instance, might go like this:
-1 | 1 -4 1 6
... | -1 5 -6
----------------------------
... | 1 -5 6 0
Next, we have
<em>x</em>² - 5<em>x</em> + 6 = (<em>x</em> - 3) (<em>x</em> - 2)
so that, in addition to <em>x</em> = -1, the other two zeros of <em>p(x)</em> are <em>x</em> = 3 and <em>x</em> = 2
