Use synthetic division to divide.
$\left( 5 x ^ { 3 } + 27 x ^ { 2 } + 5 x - 25 \right) \div ( x + 5 )$
A) $5 x ^ { 2 } + 2 x + 5 , x \neq - 5$
B) $5 x ^ { 2 } + 2 x - 5 , x \neq - 5$
C) $5 x ^ { 2 } - 2 x - 5 , x \neq - 5$
D) $2 x ^ { 2 } - 5 x + 5 , x \neq - 5$
E) $2 x ^ { 2 } - 5 x - 5 , x \neq - 5$

Question

Use synthetic division to divide. 
$\left( 5 x ^ { 3 } + 27 x ^ { 2 } + 5 x - 25 \right) \div ( x + 5 )$  
A) $5 x ^ { 2 } + 2 x + 5 , x \neq - 5$
B) $5 x ^ { 2 } + 2 x - 5 , x \neq - 5$
C) $5 x ^ { 2 } - 2 x - 5 , x \neq - 5$
D) $2 x ^ { 2 } - 5 x + 5 , x \neq - 5$
E) $2 x ^ { 2 } - 5 x - 5 , x \neq - 5$

Quizplus · Accepted Answer

To use synthetic division to divide $5x^3 + 27x^2 + 5x - 25$ by $x + 5$, we set up the division with -5 (the root of $x + 5 = 0$). The coefficients of the polynomial are brought down: 5, 27, 5, -25. Synthetic division proceeds as follows:1. Bring down the leading coefficient (5).2. Multiply -5 by the number just written down (5), getting -25, and write this under the second coefficient (27). Add them together to get 2.3. Multiply -5 by the new number (2), getting -10, and write this under the third coefficient (5). Add them together to get -5.4. Multiply -5 by the new number (-5), getting 25, and write this under the fourth coefficient (-25). Add them together to get 0, indicating no remainder.The result of the division is the polynomial written from the numbers obtained: $5x^2 + 2x - 5$, confirming that the correct answer is B) $5x^2 + 2x - 5, x \neq -5$.

Use Synthetic Division to Divide (5x3+27x2+5x−25)÷(x+5)\left( 5 x ^ { 3 } + 27 x ^ { 2 } + 5 x - 25 \right) \div ( x + 5 )(5x3+27x2+5x−25)÷(x+5)

Use Synthetic Division to Divide $\left( 5 x ^ { 3 } + 27 x ^ { 2 } + 5 x - 25 \right) \div ( x + 5 )$