Divide: Left Parenthesis negative 7 x plus x-squared plus 15 Right Parenthesis divided by Left Parenthesis negative 3 plus x Right Parenthesis
A. x minus 4 plus Start Fraction 3 over x minus 3 End Fraction
B. x minus 7 minus 5
C. x minus 4 minus Start Fraction 3 over x minus 3 End Fraction
D. x minus 7 minus Start Fraction 15 over x minus 3 End Fraction
To solve this problem, we need to use long division or synthetic division. We will use long division:
x - 4
-------------------------
-3 + x | x^2 + x - 7x + 15
- x^2 - 3x
------------
-10x + 15
-(-10x + 30)
---------------
-15
Therefore, the answer is:
(x^2 + x - 7x + 15) / (-3 + x) = x - 4 - 15 / (x - 3)
So the correct answer is D. x minus 7 minus Start Fraction 15 over x minus 3 End Fraction.
AAAaannndd the bot gets it wrong yet again!
The problem is
Left Parenthesis negative 7 x plus x-squared plus 15 Right Parenthesis divided by Left Parenthesis negative 3 plus x Right Parenthesis
(x^2-7x+15)/(x-3) = x-4 + 3/(x-3)
So, choice A
Thank you for pointing out the mistake. You are correct, the answer is A.
To divide the expression, we can follow these steps:
1. Start by factoring the numerator and the denominator. The numerator is a quadratic expression, so we need to find two numbers whose sum is 1 (-7 + 15) and whose product is -105 (-7 * 15). These numbers are -5 and -21. We can rewrite the numerator as x^2 - 5x - 21.
2. Now we have (x^2 - 5x - 21) / (-3 + x) as the division expression.
3. To simplify the division expression, we can use polynomial long division or synthetic division. Let's use synthetic division.
Start by setting up the synthetic division like this:
-3 | 1 -5 -21
|_________
Next, we'll write the coefficients of the numerator in descending order, leaving out any missing terms (such as x terms with a coefficient of 0).
4. Now perform the synthetic division:
-3 | 1 -5 -21
|_________
1 -8 15
(bring down the 1, multiply -3 by 1 and add it to -5 to get -8, multiply -3 by -8 and add it to -21 to get 15)
5. The result of the synthetic division is a quotient of 1 - 8x + 15/(x - 3). Rewriting this, we have 1 - 8x + 15/(x - 3) as the simplified division expression.
Now let's compare this simplified expression to the given options:
A. x - 4 + 3/(x - 3)
B. x - 7 - 5
C. x - 4 - 3/(x - 3)
D. x - 7 - 15/(x - 3)
The correct answer would be option C. x - 4 - 3/(x - 3).