Question

Select the correct answer. One factor of the polynomial 3x^(3)+20x^(2)-21x+88 is (x+8). What is the other factor of the polynomial? (Note: Use long division. )

Answer 1

To find the other factor of the polynomial 3x^3 + 20x^2 - 21x + 88 given (x + 8) as one factor, we use long division method. The result of the division gives the other factor, which is 3x^2 - 4x + 11.

Step-by-step explanation:

The problem given is to find the other factor of the polynomial 3x^3 + 20x^2 - 21x + 88 given that one of the factors is (x + 8). To do this, we will use long division to divide the polynomial by the known factor.

Steps of the long division:

1. Divide the first term of the polynomial by the first term of the factor, in this case, 3x^3 / x which gives us 3x^2.
2. Multiply the entire factor (x + 8) by this result (3x^2) and subtract the resultant from the polynomial.
3. The result of this subtraction gives a new polynomial. Repeat steps 1 and 2 with this new polynomial until you end with a degree less than the degree of the divisor (x + 8), which will be the remainder. The quotient from this division process is the other factor of the polynomial.

After completing these steps, we find the other factor to be 3x^2 - 4x + 11.

Answer 2

To find the other factor of the polynomial given (x+8) as one known factor, perform long division of the polynomial by (x+8) to obtain the quotient, which represents the other factor.

Step-by-step explanation:

To find the other factor of the polynomial 3x3+20x2-21x+88, given that (x+8) is one factor, we can use long division. We divide the polynomial by the factor (x+8).

The division process will give us a quotient, which is the other factor we're looking for. The steps are as follows:

1. Divide the first term of the polynomial (3x3) by the first term of the factor (x), which gives us 3x2.
2. Multiply (x+8) by 3x2 and subtract the result from the polynomial.
3. Bring down the next term of the polynomial and repeat the process until we've brought down all terms.
4. The remainder should be zero since (x+8) is a factor of the polynomial, and the quotient is the other factor we are seeking.

Performing these steps, we find the corresponding other factor of the polynomial, which will be a quadratic expression.