Use synthetic division to find P(-2) for P(x)=(x^4)-(5x^3)+3x+2. Show all steps.
To find P(-2) for P(x)=(x^4)-(5x^3)+3x+2 using synthetic division, we set up the coefficients of the polynomial in the synthetic division box and perform the division as follows:
-2 | 1 -5 0 3 2
Bring down the first coefficient:
1
Multiply -2 by 1:
-2
Add the second coefficient:
1 + (-2) = -1
Multiply -2 by -1:
2
Add the third coefficient:
0 + 2 = 2
Multiply -2 by 2:
-4
Add the fourth coefficient:
3 + (-4) = -1
Multiply -2 by -1:
2
Add the fifth coefficient:
2 + 2 = 4
Therefore, the remainder is 4, and P(-2) is equal to 4.