Question

9x³ -7x+2, x-(1)/(3). Find the quotient and remainder

Answer 1

To find the quotient and remainder, perform polynomial long division using the given polynomial and divisor.

Step-by-step explanation:

To find the quotient and remainder, we need to perform polynomial long division using the given polynomial, 9x³ - 7x + 2, and the divisor, x - (1/3).

1. Start by dividing the first term of the dividend, 9x³, by the first term of the divisor, x. This gives us 9x² as the first term of the quotient.
2. Multiply the entire divisor, x - (1/3), by the first term of the quotient, 9x². This gives us 9x³ - 3x² as the first term of the product.
3. Subtract the product from the dividend: 9x³ - 7x + 2 - (9x³ - 3x²). This gives us -3x² - 7x + 2 as the new dividend.
4. Repeat the process by dividing the first term of the new dividend, -3x², by the first term of the divisor, x. This gives us -3x as the second term of the quotient.
5. Multiply the entire divisor by the second term of the quotient. This gives us -3x³ + x² as the second term of the product.
6. Subtract the product from the new dividend: -3x² - 7x + 2 - (-3x³ + x²). This gives us -8x² - 7x + 2 as the new dividend.

Continue this process until the degree of the new dividend is less than the degree of the divisor.

The final quotient is 9x² - 3x - 3, and the remainder is -8x² - 7x + 2.