Use synthetic division to find P(3) for P(x) = x4 – 6x3 – 4x2 – 6x – 2
3
–137
299
–47
To use synthetic division to find P(3) for the given polynomial P(x) = x^4 – 6x^3 – 4x^2 – 6x – 2, follow these steps:
1. Set up the synthetic division table by writing down the coefficients of the polynomial in decreasing order. In this case, the coefficients are: 1, -6, -4, -6, and -2.
1 | -6 -4 -6 -2
2. Write down the value you want to evaluate the polynomial at, in this case, 3, to the left of the division table.
3 1 | -6 -4 -6 -2
3. Bring down the first coefficient, which is 1, directly below the line.
3 1 | -6 -4 -6 -2
1
4. Multiply the value below the line (1) by the value to the left (3), and write the result (-3) above the second coefficient.
3 1 | -6 -4 -6 -2
-3
1
5. Add the result (-3) to the second coefficient (-6), and write the sum (-9) below the line.
3 1 | -6 -4 -6 -2
-3
1 -9
6. Multiply the value below the line (-9) by the value to the left (3), and write the result (-27) above the third coefficient.
3 1 | -6 -4 -6 -2
-3 27
1 -9
7. Add the result (-27) to the third coefficient (-4), and write the sum (-31) below the line.
3 1 | -6 -4 -6 -2
-3 27
1 -9 -31
8. Multiply the value below the line (-31) by the value to the left (3), and write the result (-93) above the fourth coefficient.
3 1 | -6 -4 -6 -2
-3 27 -93
1 -9 -31
9. Add the result (-93) to the fourth coefficient (-6), and write the sum (-99) below the line.
3 1 | -6 -4 -6 -2
-3 27 -93 -99
1 -9 -31
10. Multiply the value below the line (-99) by the value to the left (3), and write the result (-297) above the last coefficient.
3 1 | -6 -4 -6 -2
-3 27 -93 -99
1 -9 -31 -297
11. Add the result (-297) to the last coefficient (-2), and write the sum (-299) below the line.
3 1 | -6 -4 -6 -2
-3 27 -93 -99
1 -9 -31 -297
-299
The number below the line, -299, is the result of P(3) using synthetic division. Therefore, P(3) = -299.
Thank you
Online "^" is used to indicate an exponent, e.g., x^2 = x squared
3^4 - 6(3^3) - 4(3^2) - 18 - 2 = ?