Question

Consider the polynomial function P(x)=x^3+2x^2+2x-5. Divide P by the divisor (x-1)

Answer 1

To divide P(x) = x^3 + 2x^2 + 2x - 5 by (x - 1), use long division method. The quotient is x^2 + 3x + 5 with a remainder of 0.

Step-by-step explanation:

To divide the polynomial function P(x) = x^3 + 2x^2 + 2x - 5 by the divisor (x - 1), we can use the long division method.

1. First, divide the leading term of P(x) by the leading term of the divisor. In this case, x^3 ÷ x = x^2.
2. Multiply the entire divisor (x - 1) by the result from step 1, x^2, and subtract it from P(x).
3. Repeat step 1 with the new polynomial obtained from step 2.
4. Continue this process until there are no more terms to divide.

The result of dividing P(x) by (x - 1) is a quotient of x^2 + 3x + 5 and a remainder of 0.