Question

(12x^5-9x^4+8x^2-6x):(4x^2-3x)-Выполнить деление столбиком

Answer 1

$12 {x}^{5} - 9 {x}^{4} + 8 {x}^{2} - 6x = 3 {x}^{3} (4 {x}^{2} - 3x) + 2(4 {x}^{2} - 3x) = (3 {x}^{3} + 2)(4 {x}^{2} - 3x)$

Answer 2

To perform long division with polynomials, follow these steps:

Step 1: Arrange the polynomial division in descending order (highest exponent to lowest exponent).

Step 2: Divide the first term of the dividend by the first term of the divisor, and write the result above the dividend. This will be the first term of the quotient.

Step 3: Multiply the divisor by the first term of the quotient, and write the result below the first two terms of the dividend.

Step 4: Subtract the result from Step 3 from the first two terms of the dividend.

Step 5: Bring down the next term of the dividend.

Step 6: Repeat steps 2 to 5 until all terms of the dividend have been used or until the degree of the remaining dividend terms is less than the degree of the divisor.

Let's apply these steps to the given problem:

Divide (12x^5 - 9x^4 + 8x^2 - 6x) by (4x^2 - 3x).

scssCopy code
                  3x^3 + 3x^2 - 2x
           ___________________________
4x^2 - 3x |  12x^5 - 9x^4 + 8x^2 - 6x
             -(12x^5 - 9x^4)
             _________________
                       0 + 8x^2 - 6x
                       -(8x^2 - 6x)
                       ______________
                                       0

The result of the division is: 3x^3 + 3x^2 - 2x.