Final answer:
To divide (x² + 6x + 8) by (x + 2) using long division, follow the steps: divide the highest degree term of the dividend by the highest degree term of the divisor, multiply the quotient by the divisor, subtract this from the dividend, and repeat until the remainder is zero or the degree of the remainder is less than the degree of the divisor.
Step-by-step explanation:
Dividing polynomials using long division: To divide (x² + 6x + 8) by (x + 2), we first divide the highest degree term of the dividend, which is x², by the highest degree term of the divisor, which is x. This gives us x. We then multiply x by the divisor (x + 2) to obtain x² + 2x. We subtract this result from the original dividend (x² + 6x + 8) to get 4x + 8. We then bring down the next term from the dividend, which is 4x. We repeat the process of dividing the highest degree term of the new dividend (4x + 8) by the divisor (x + 2), which gives us 4. We multiply 4 by the divisor (x + 2) to obtain 4x + 8. We subtract this from the new dividend to get 0. Therefore, the quotient q(x) is x + 4.
Example: Dividing (x² + 6x + 8) by (x + 2) gives a quotient of x + 4.
Key Points: - Long division is a method used to divide polynomials. - The divisor must be in the form of (x + c), where c is any number. - The quotient is obtained by dividing the highest degree term of the dividend by the highest degree term of the divisor. - Repeat the process until the remainder is zero or the degree of the remainder is less than the degree of the divisor.
Learn more about Dividing polynomials