Using synthetic division, find the quotient Q(x) and the remainder R if the polynomial P(x) = x3 − 2x2 − 3x + 18 is divided by (
x + 2).
1 answer:
Answer:
quotient: x^2 - 4x + 5
remainder: 8
Explanation:
1) Given
p(x) = x^3 - 2x^2 - 3x + 18
divisor: x + 2
2) Write the coefficients of p(x) in order:
1 -2 -3 18
3) dividing by x + 2 => run the division for x = - 2
4) division
| 1 -2 -3 +18
|
-2 | -2 +8 - 10
-----------------------------------
1 -4 +5 +8
The last digit is the remainder, the others are the coefficients of the quotient:
=>
quotient = x^2 - 4x + 5
remainder = 8
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