Question

Given the polynomial P(x) = x³+4x²-7x-10, ind a polynomial Q(x) such that (x - 2)Q(x) = P(x).

Answer 1

To find the polynomial Q(x) such that (x - 2)Q(x) = P(x), use polynomial long division. The polynomial Q(x) is x² + 6x + 18.

Step-by-step explanation:

To find the polynomial Q(x) such that (x - 2)Q(x) = P(x), we need to divide P(x) by (x - 2). We can use polynomial long division to divide P(x) by (x - 2). Here's the step-by-step process:

1. Write the polynomial P(x) in descending order of exponents:
2. Divide the leading term of P(x) by the leading term of (x - 2), which is x:
3. Multiply the divisor (x - 2) by the quotient term, which is (x² + 6x + 18):
4. Subtract the product from the dividend:
5. Bring down the next term:
6. Repeat the division process until there is no remainder:

Therefore, the polynomial Q(x) such that (x - 2)Q(x) = P(x) is Q(x) = x² + 6x + 18.