Divide by synthetic division

(x^4-15x^2 +38x-60)/(x-3)

Can someone please help with this.

visit here for all the details:

http://www.mathportal.org/calculators/polynomials-solvers/synthetic-division-calculator.php

Certainly! Synthetic division is a method used to divide a polynomial by a linear expression. I can guide you through the steps:

Step 1: Set up the synthetic division table by writing the coefficients of the polynomial in descending order. In this case, the polynomial is \(x^4 - 15x^2 + 38x - 60\). So, the coefficients are 1, 0, -15, 38, -60.

| 1 | 0 | -15 | 38 | -60 |
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Step 2: Bring down the first coefficient, which is 1.

| 1 | 0 | -15 | 38 | -60 |
1

Step 3: Multiply the value you brought down by the divisor (x - 3) and write the result underneath the next coefficient.

| 1 | 0 | -15 | 38 | -60 |
1 * 3

| 1 | 3 | | |
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Step 4: Add the result to the next coefficient (0) and write the sum underneath the line.

| 1 | 0 | -15 | 38 | -60 |
1 * 3
0 + 3

| 1 | 3 | -15 | |
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Step 5: Repeat steps 3 and 4 until you reach the last coefficient.

| 1 | 0 | -15 | 38 | -60 |
1 * 3
0 + 3
3 * 3
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| 1 | 3 | -15 | 13 | -21 |

Step 6: The numbers in the bottom row represent the coefficients of the quotient. The last number (-21) is the remainder.

The quotient is \(x^3 + 3x^2 - 15x + 13\) and the remainder is -21.

So, the result of dividing \(x^4 - 15x^2 + 38x - 60\) by \(x - 3\) using synthetic division is \(x^3 + 3x^2 - 15x + 13\) with a remainder of -21.