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 (since we're dividing by $x + 5$, we use the opposite sign). The coefficients of the polynomial are brought down: 5, 27, 5, -25. Performing synthetic division:1. Bring down the 5 (leading coefficient) to start.2. Multiply -5 by 5 (the number just brought down), which gives -25. Write this under the second coefficient (27).3. Add the numbers in the second column: 27 + (-25) = 2.4. Repeat the process: Multiply -5 by the new number (2), giving -10, and add this to the next coefficient (5), resulting in -5.5. Finally, multiply -5 by -5 (the result from the previous step), giving 25, and add this to the last coefficient (-25), resulting in 0.The result of the synthetic division is the quotient $5x^2 + 2x - 5$, with a remainder of 0, indicating that $x + 5$ is a factor of the original polynomial. Therefore, the correct answer is $5x^2 + 2x - 5, x \neq -5$.

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 $\left( 5 x ^ { 3 } + 27 x ^ { 2 } + 5 x - 25 \right) \div ( x + 5 )$