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Answer :
Sure! Let's go through the problem of synthetic division step by step.
To perform synthetic division on the polynomial represented by the coefficients [2, 7, 5] using the divisor -1, follow these steps:
1. Write Down the Coefficients: Start with the coefficients of the polynomial (2, 7, 5). These represent the polynomial [tex]\(2x^2 + 7x + 5\)[/tex].
2. Set Up the Division: Write the divisor, which is -1, to the left of the coefficients.
3. Bring Down the Leading Coefficient: Begin by bringing down the first coefficient (2) as it is. This 2 is the first coefficient of the quotient.
4. Multiply and Add:
- Multiply the divisor (-1) by the value you just brought down (2), which gives you -2.
- Add this result (-2) to the next coefficient (7). The sum is 5.
- Write this result (5) as the next coefficient of the quotient.
5. Repeat the Process:
- Multiply the divisor (-1) by the new number (5) you just calculated, which gives you -5.
- Add this result (-5) to the last coefficient (5) of the original polynomial. The sum is 0.
6. Read the Quotient: The quotient is formed by the first two numbers you obtained (2 and 5). Therefore, the polynomial quotient is [tex]\(2x + 5\)[/tex].
So, the quotient of the synthetic division in polynomial form is [tex]\(2x + 5\)[/tex], which corresponds to option B.
To perform synthetic division on the polynomial represented by the coefficients [2, 7, 5] using the divisor -1, follow these steps:
1. Write Down the Coefficients: Start with the coefficients of the polynomial (2, 7, 5). These represent the polynomial [tex]\(2x^2 + 7x + 5\)[/tex].
2. Set Up the Division: Write the divisor, which is -1, to the left of the coefficients.
3. Bring Down the Leading Coefficient: Begin by bringing down the first coefficient (2) as it is. This 2 is the first coefficient of the quotient.
4. Multiply and Add:
- Multiply the divisor (-1) by the value you just brought down (2), which gives you -2.
- Add this result (-2) to the next coefficient (7). The sum is 5.
- Write this result (5) as the next coefficient of the quotient.
5. Repeat the Process:
- Multiply the divisor (-1) by the new number (5) you just calculated, which gives you -5.
- Add this result (-5) to the last coefficient (5) of the original polynomial. The sum is 0.
6. Read the Quotient: The quotient is formed by the first two numbers you obtained (2 and 5). Therefore, the polynomial quotient is [tex]\(2x + 5\)[/tex].
So, the quotient of the synthetic division in polynomial form is [tex]\(2x + 5\)[/tex], which corresponds to option B.
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