Question

5.41. a) 1-16a² 4a²+ 10a +25 : 4a-1 8a³ - 125 062 16g²​

Answer 1

Ответ:

=1-64а⁴+65/4а-18а³-125 062 16g²

Объяснение:

1-16a² 4a²+ 10a +25 : 4a-1 8a³ - 125 062 16g²= 1-64а⁴+10а+25/4а -18a³ - 125 062 16g²=1-64а⁴+65/4а-18а³-125 062 16g²

Answer 2

To perform this polynomial division, we'll divide the numerator by the denominator. Here's the division step by step:

Dividend: 1 - 16a² + 4a² + 10a + 25 Divisor: 4a - 1

Step 1: Divide the first term of the dividend (1) by the first term of the divisor (4a). 1 / (4a) = 1/4a

Step 2: Multiply the divisor (4a - 1) by the result from step 1 (1/4a) and subtract it from the dividend. (4a - 1) * (1/4a) = 1 - 1/4a Subtract this from the dividend: 1 - 16a² + 4a² + 10a + 25 - (1 - 1/4a) = -16a² + 4a² + 10a + 25 + 1/4a

Step 3: Continue the process with the new expression: Dividend: -16a² + 4a² + 10a + 25 + 1/4a Divisor: 4a - 1

Repeat steps 1 and 2:

Step 1: Divide the first term of the new dividend (-16a²) by the first term of the divisor (4a). -16a² / (4a) = -4a

Step 2: Multiply the divisor (4a - 1) by the result from step 1 (-4a) and subtract it from the new dividend. (4a - 1) * (-4a) = -16a² + 4a Subtract this from the new dividend: -16a² + 4a² + 10a + 25 + 1/4a - (-16a² + 4a) = 4a² + 10a + 25 + 1/4a + 4a

Now, we continue with this new expression:

Dividend: 4a² + 10a + 25 + 1/4a + 4a Divisor: 4a - 1

Step 1: Divide the first term of the new dividend (4a²) by the first term of the divisor (4a). 4a² / (4a) = a

Step 2: Multiply the divisor (4a - 1) by the result from step 1 (a) and subtract it from the new dividend. (4a - 1) * a = 4a² - a Subtract this from the new dividend: 4a² + 10a + 25 + 1/4a + 4a - (4a² - a) = 11a + 25 + 1/4a

Now, we have:

Dividend: 11a + 25 + 1/4a Divisor: 4a - 1

Step 1: Divide the first term of the new dividend (11a) by the first term of the divisor (4a). 11a / (4a) = 11/4

Step 2: Multiply the divisor (4a - 1) by the result from step 1 (11/4) and subtract it from the new dividend. (4a - 1) * (11/4) = 11a - 11/4 Subtract this from the new dividend: 11a + 25 + 1/4a - (11a - 11/4) = 25 + 1/4a + 11/4

So, the result of the division is:

(25 + 1/4a + 11/4)/(4a - 1)