use synthetic division to find (2x^3 -5x^2 +7x-1) divided (x-1)
hard to line up the columns in this format, so I leave it up to you to line them up
1 │ 2 -5 7 -1
...... 2-3 4
....2 -3 4 3
so (2x^3 -5x^2 +7x-1)÷ (x-1) = 2x^2 - 3x + 4 with a remainder of 3
or (2x^3 -5x^2 +7x-1) = (x-1)(2x^2 - 3x + 4) + 3
To use synthetic division to divide a polynomial by a linear expression, we follow these steps:
Step 1: Write the polynomial in descending order and ensure that all powers of x are included, even if the coefficient is zero. So, in this case, we can rewrite the polynomial as:
2x^3 - 5x^2 + 7x - 1
Step 2: Write the divisor (x-1) next to the polynomial, and set it up in synthetic division form:
1 | 2 -5 7 -1
Step 3: Bring down the first coefficient, which is 2 in this case.
1 | 2 -5 7 -1
|
2
Step 4: Multiply the divisor (1) by the number you brought down (2), and write the result below the next coefficient in the polynomial.
1 | 2 -5 7 -1
| 2
__________
2
Step 5: Add the result obtained in the previous step to the next coefficient in the polynomial, and write the sum below the line.
1 | 2 -5 7 -1
| 2
__________
2 -3
Step 6: Repeat steps 4 and 5 until you have performed the process for all the coefficients.
1 | 2 -5 7 -1
| 2 -3
__________
2 -3 4
Step 7: Read the final row of numbers, which corresponds to the coefficients of the quotient. In this case, the final row is 2 -3 4.
Therefore, the quotient of (2x^3 - 5x^2 + 7x - 1) divided by (x-1) is 2x^2 - 3x + 4.