SOLUTION: Use synthetic division for the given polynomial f(x) = 2x3 -5x2- 4x + 3, find all the solutions if the function is completed. a) f(x) =0 b) f(x+2)=0 d) f(2x) = 0 Please sho

Question 68183This question is from textbook Precalculus
: Use synthetic division for the given polynomial
f(x) = 2x3 -5x2- 4x + 3, find all the solutions if the function is completed.
a) f(x) =0
b) f(x+2)=0
d) f(2x) = 0
Please show the work. I have the answer, I just need to confirm I did all of the steps correct.

This question is from textbook Precalculus

Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
Use synthetic division for the given polynomial
f(x) = 2x3 -5x2- 4x + 3, find all the solutions if the function is completed.
a) f(x) =0
TEST F(1),F(-1),F(3),F(-3) ETC..
F(-1)=-2-5+4+3=0..........X=-1 IS A SOLUTION
-1|2,-5,-4,+3
..|0,-2,+7,-3
------------------
...2,-7,+3,0
2X^2-7X+3=0
=2X^2-6X-X+3=0
=2X(X-3)-1(X-3)=0
(2X-1)(X-3)=0
HENCE X=1/2 ...OR...3....OR......-1

b) f(x+2)=0
PUT Y=X+2.....F(Y)=0....SO....X+2=Y=-1..........OR.......1/2....OR........3
X=-3..........OR...........-3/2............OR........1
d) f(2x) = 0
PUT Y=2X.....F(Y)=0.......2X=Y=-1..........OR........1/2..........OR.......3
X=-1/2......OR...........1/4..............OR.........3/2
Please show the work. I have the answer, I just need to confirm I did all of the steps correct.

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