QQuestionMathematics
QuestionMathematics
Complete the synthetic division problem below:
2| 1 5 −14
What is the quotient in polynomial form?
A. x+ 5
B. x−7
C. x+ 7
D. x−5
12 months agoReport content
Answer
Full Solution Locked
Sign in to view the complete step-by-step solution and unlock all study resources.
Step 1:I'll solve this synthetic division problem step by step:
Step 2:: Identify the divisor and dividend
- The dividend is the polynomial $$1x^{2} + 5x - 14
- The divisor is 2
Step 3:: Set up synthetic division
- Bring down the first coefficient (1) - Multiply and bring down the next values
Step 4:: Perform synthetic division
\begin{array}{r}
2 \enclose{longdiv}{1 \quad 5 \quad - 14} \ \underline{2 \quad 14} \ 1 \quad 7 \quad 0 \end{array}
Step 5:: Interpret the result
- The first row is the original coefficients - The second row shows the multiplications - The bottom row gives the coefficients of the quotient
Step 6:: Write the quotient polynomial
- The bottom row gives us $$1x + 7
- This simplifies to x + 7
Final Answer
Key Insights: - In synthetic division, we're dividing the polynomial by (x - 2) - The bottom row represents the coefficients of the quotient - The last number (0) would represent the remainder, which is zero in this case
Need Help with Homework?
Stuck on a difficult problem? We've got you covered:
- Post your question or upload an image
- Get instant step-by-step solutions
- Learn from our AI and community of students