If there are real roots to be found for this polynomial, the Rational Root Theorem and synthetic division are the best way to find them. I teach from a book that uses c and d for the possible roots of the polynomial. C is our constant, 2, and d is the leading coefficient, 1. The factors of 2 are +/- 1 and +/-2. The factors for 1 are +/-1 only. Meaning, in all, there are 4 possibilities as roots for this polynomial. But there are only 3 total (because our polynomial is a third degree), so we have to find the first one, at least, from our possibilities above. Let's try x = -1, factor form (x + 1). If there is no remainder when we do the synthetic division, then -1 is a root. Put -1 outside the "box" and the coefficients from the polynomial inside: -1 (1 2 -1 -2). Bring down the first coefficient of 1 and multiply it by the -1 outside to get -1. Put that -1 up under the 2 and add to get 1. Multiply 1 times the -1 to get -1 and put that -1 up under the -1 and add to get -2. -1 times -2 is 2, and -2 + 2 = 0. So we have our first root of (x+1). The numbers we get when we do the addition along the way are the coefficients of our new polynomial, the depressed polynomial (NOT a sad one cuz it hates math, but a new polynomial that is one degree less than that of which we started!). The new polynomial is 
. That can also be factored to find the remaining 2 roots. Use standard factoring to find that the other 2 solutions are (x+2) and (x-1). Our solutions then are x = -2, -1, 1, choice B from above.
Mia enlarged a plan for an outdoor stage. The original plan is shown below. She dilated the outdoor stage by a scale factor of 4
with the center of dilation at the origin. Which ordered pair will be the coordinates of one of the new vertices? A (2,1) B (8,16) C (32,4) D (32,16)
2 answers:
Answer:
D (32,16)
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one. Please see the attached photo.
In the photo, the four vertices are:
(-5,4) by a scale factor of 4 (-20, 16)
(8, 4) by a scale factor of 4 (32, 16)
(-6, -2) by a scale factor of 4 (-24, -8)
(8, -2) by a scale factor of 4 (31, -8)
So only D is correct.
Hope it will find you well.
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