SOLUTION: Which polynomial gives a quotient of (3x2 + 2x + 4) and a remainder of 19 when divided by (2x – 3)? A. 6x3 – 5x2 + 2x B. 6x3 – 5x2 + 4x + 7 C. 6x3 – 5x2 + 2x + 7 D. 6x3 +

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Question 982312: Which polynomial gives a quotient of (3x2 + 2x + 4) and a remainder of
19 when divided by (2x – 3)?
A. 6x3 – 5x2 + 2x
B. 6x3 – 5x2 + 4x + 7
C. 6x3 – 5x2 + 2x + 7
D. 6x3 + 5x2 + 2x + 7
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
Divide each of those choices by 2x-3, using polynomial division; and see which gives the specified quotient and remainder.

Here, testing just choice A:


_____________|
_____________|_________3x^2_______2x__________4__________(the quotient line)
_____________|_______________________________________________
_____________|
2x-3_________|________6x^3_______-5x^2_________+2x________(divisor on left, dividend on right)
______________________6x^2_______-9x^2
______________________________________
______________________0__________4x^2___________2x
_________________________________4x^2___________-6x
___________________________________________________
_________________________________0______________8x________0
________________________________________________8x________-12
______________________________________________________________
_________________________________________________0_________12

Remainder of 12;
Not choice A.


You try the others.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Which polynomial gives a quotient of (3x2 + 2x + 4) and a remainder of
19 when divided by (2x – 3)?
A. 6x3 – 5x2 + 2x
B. 6x3 – 5x2 + 4x + 7
C. 6x3 – 5x2 + 2x + 7
D. 6x3 + 5x2 + 2x + 7
Whichever polynomial results in:  is your polynomial. 

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