Solve. (–10x3 + 30x – 20) ÷ (–5x + 5)

• 2x2 – 2x + 4
• –2x2 – 2x – 4
• –2x2 + 2x + 4
• 2x2 + 2x – 4

How?

To solve the given problem, we need to perform polynomial long division. Here are the steps to solve for (–10x^3 + 30x – 20) ÷ (–5x + 5):

Step 1: Arrange the terms in descending order of degree for both the dividend and divisor:
Dividend: –10x^3 + 30x – 20
Divisor: –5x + 5

Step 2: Divide the first term of the dividend by the first term of the divisor:
(–10x^3 ÷ –5x) = 2x^2.

Step 3: Multiply the divisor by the quotient obtained in Step 2:
(–5x + 5) × 2x^2 = –10x^3 + 10x^2.

Step 4: Subtract the result obtained in Step 3 from the dividend:
(–10x^3 + 30x – 20) - (–10x^3 + 10x^2) = 30x – 20 – 10x^2.

Step 5: Repeat Steps 2-4 with the new expression obtained in Step 4:
(30x – 20 – 10x^2) ÷ (–5x + 5).

Step 6: Divide the first term of the new expression (30x) by the first term of the divisor (–5x):
(30x ÷ –5x) = –6.

Step 7: Multiply the divisor by the quotient obtained in Step 6:
(–5x + 5) × –6 = 30x – 30.

Step 8: Subtract the result obtained in Step 7 from the new expression:
(30x – 20 – 10x^2) - (30x – 30) = –20 – 10x^2 + 30.

Step 9: Simplify the expression obtained in Step 8:
–20 – 10x^2 + 30 = –10x^2 + 10.

Therefore, the quotient is –10x^2 + 10.

Comparing this result with the given options, we see that none of the options match the quotient obtained. So, the solutions provided do not match the result of the division.

. (x-4) - (2x+5) Simplify the expression above. Which of the following is correct?

A. -X-9
B. -x + 1
C. 2x2 -3x -20
D. -2x2 + 13x-20

-10 (x^3 - 3 x + 2) /[-5(x-1)]

2 (x^3 - 3 x + 2) / (x-1)

2 (x^2+x-2)(x-1)/(x-1)

2 x^2 + 2 x -4