Question

Consider the polynomial function f(x)=3x^(2)+8x-4. a. Dlvide f by x-2.

Answer 1

To divide f(x) by x-2, use polynomial long division. The quotient is 3x + 14 and the remainder is 24.

Step-by-step explanation:

To divide f(x) by x-2, we can use polynomial long division. Here are the steps:

1. Write the polynomial f(x) = 3x^2 + 8x - 4.
2. Set up the long division with the divisor x-2 on the left and the dividend 3x^2 + 8x - 4 on the right.
3. Divide the first term of the dividend (3x^2) by the first term of the divisor (x) to get 3x. Write this above the dividing line.
4. Multiply the divisor (x-2) by the quotient (3x) to get 3x^2 - 6x.
5. Subtract 3x^2 - 6x from the dividend 3x^2 + 8x - 4 to get 14x - 4. Write this below the line.
6. Bring down the next term, which is 14x, and divide it by the first term of the divisor (x) to get 14.
7. Multiply the divisor (x-2) by the quotient (14) to get 14x - 28.
8. Subtract 14x - 28 from the current remainder 14x - 4 to get 24. Write this below the line.
9. Since the degree of the remainder (24) is less than the degree of the divisor (x-2), we cannot proceed further.

Therefore, the quotient is 3x + 14 and the remainder is 24. So, f(x) divided by x-2 is equal to 3x + 14 with a remainder of 24. This can be written as:

f(x) = (x-2)*(3x + 14) + 24.