Use synthetic division to divide. x 4 − 4 x 2 + 6 x − 4 \frac { x ^ { 4 } - 4 x ^ { 2 } + 6 } { x - 4 } x − 4 x 4 − 4 x 2 + 6 A) x 3 − 2 x 2 + 6 x − 24 + 18 x − 4 x ^ { 3 } - 2 x ^ { 2 } + 6 x - 24 + \frac { 18 } { x - 4 } x 3 − 2 x 2 + 6 x − 24 + x − 4 18 B) x 3 − 4 x 2 + 12 x − 48 + 198 x − 4 x ^ { 3 } - 4 x ^ { 2 } + 12 x - 48 + \frac { 198 } { x - 4 } x 3 − 4 x 2 + 12 x − 48 + x − 4 198 C) x 3 + 6 x + 10 + 28 x − 4 x ^ { 3 } + 6 x + 10 + \frac { 28 } { x - 4 } x 3 + 6 x + 10 + x − 4 28 D) x 3 + x 2 + x + 1 + 48 x − 4 x ^ { 3 } + x ^ { 2 } + x + 1 + \frac { 48 } { x - 4 } x 3 + x 2 + x + 1 + x − 4 48 E) x 3 + 4 x 2 + 12 x + 48 + 198 x − 4 x ^ { 3 } + 4 x ^ { 2 } + 12 x + 48 + \frac { 198 } { x - 4 } x 3 + 4 x 2 + 12 x + 48 + x − 4 198

Question

Use synthetic division to divide.   x 4 − 4 x 2 + 6 x − 4 \frac { x ^ { 4 } - 4 x ^ { 2 } + 6 } { x - 4 } x − 4 x 4 − 4 x 2 + 6 ​ A)    x 3 − 2 x 2 + 6 x − 24 + 18 x − 4 x ^ { 3 } - 2 x ^ { 2 } + 6 x - 24 + \frac { 18 } { x - 4 } x 3 − 2 x 2 + 6 x − 24 + x − 4 18 ​ B)    x 3 − 4 x 2 + 12 x − 48 + 198 x − 4 x ^ { 3 } - 4 x ^ { 2 } + 12 x - 48 + \frac { 198 } { x - 4 } x 3 − 4 x 2 + 12 x − 48 + x − 4 198 ​ C)    x 3 + 6 x + 10 + 28 x − 4 x ^ { 3 } + 6 x + 10 + \frac { 28 } { x - 4 } x 3 + 6 x + 10 + x − 4 28 ​ D)    x 3 + x 2 + x + 1 + 48 x − 4 x ^ { 3 } + x ^ { 2 } + x + 1 + \frac { 48 } { x - 4 } x 3 + x 2 + x + 1 + x − 4 48 ​ E)    x 3 + 4 x 2 + 12 x + 48 + 198 x − 4 x ^ { 3 } + 4 x ^ { 2 } + 12 x + 48 + \frac { 198 } { x - 4 } x 3 + 4 x 2 + 12 x + 48 + x − 4 198 ​

Cassandra Terry · Accepted Answer

Final Answer : E, Explanation :  To use synthetic division, we first set up the division with the divisor (x - 4) on the left side and the coefficients of the dividend (x^4 - 4x^2 + 6) on the top:\begin{array}{c|cccc}4 & 1 & 0 & -4 & 0 & 6 \\hline& & 4 & 16 & 48 & 192 \\hline1 & 4 & 12 & 44 & 48 & 198 \\end{array}The bottom row represents the coefficients of the quotient, so we can see that the quotient is x^3 + 4x^2 + 12x + 48. The remainder is the number in the last position, divided by the divisor. In this case, it is 198/(x-4). Therefore, the correct answer is E.

Use synthetic division to divide. $x4−4x2+6x−4\frac { x ^ { 4 } - 4 x ^ { 2 } + 6 } { x - 4 }$

A) $\frac { 18 } { x - 4 }$
B) $\frac { 198 } { x - 4 }$
C) $\frac { 28 } { x - 4 }$
D) $\frac { 48 } { x - 4 }$
E) $\frac { 198 } { x - 4 }$

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