Final answer:
To divide the polynomial (4x² + 23x + 2) by (x + 4), use long division. The quotient is 4x + 7 and the remainder is -26.
Step-by-step explanation:
To divide the polynomial (4x² + 23x + 2) by (x + 4), we use long division. The first step is to divide the highest power term of the dividend by the highest power term of the divisor. In this case, (4x² ÷ x) = 4x. We then multiply (x + 4) by 4x to get 4x² + 16x. Subtracting this from the original dividend gives us (23x - 16x) = 7x + 2.
Next, we bring down the next term, which is 7x. Dividing (7x ÷ x) gives us 7. We multiply (x + 4) by 7 to get 7x + 28. Subtracting this from our current dividend gives us (2 - 28) = -26.
Since there are no more terms to bring down, our quotient is 4x + 7 and the remainder is -26. Therefore, the result of the division is (4x + 7) with a remainder of -26.
Learn more about Dividing polynomials