What is the simpler form of the following expression?
(6x3 – 1x2 + 1) ÷ (2x + 1)
A. –3x2 + 2x – 1
B. 3x2 – 2x + 1
C. –3x2 + 2x – 1
D. 3x3 + 2x – 1
C. –3x2 + 2x – 1
To find the simpler form of the expression (6x3 – 1x2 + 1) ÷ (2x + 1), we need to perform the division. Let's start step by step:
First, we divide the first term (6x3) of the numerator (dividend) by the first term (2x) of the denominator (divisor). This gives us 6x3 ÷ 2x = 3x2. So, the result so far is 3x2.
Next, we multiply the `divisor` (2x + 1) by the result we obtained so far (3x2). This gives us (2x + 1) * (3x2), which equals 6x3 + 3x2.
Subtracting this product (6x3 + 3x2) from the numerator (6x3 – 1x2 + 1), we get (6x3 – 1x2 + 1) - (6x3 + 3x2). Simplifying this, we have -1x2 + 1 - 3x2, which can be rewritten as (-1 - 3)x2 + 1 = -4x2 + 1.
Lastly, we divide the remaining terms (-4x2 + 1) by the divisor (2x + 1), similar to the previous step. Dividing -4x2 by 2x gives us -2x. So, we have -2x + 1.
Therefore, the simpler form of the expression (6x3 – 1x2 + 1) ÷ (2x + 1) is -2x + 1.
Thus, the correct answer is D. -2x + 1.