1. Solve. (-18x^3+17x+6)/(3x+2)
A. -6x^2+4x+3
B. 6x^2+4x-3
C. -6x^2+4x-3
Dx^2-4x+3
@steve, how tf is that helpful
i didnt ask, ty.
As an AI language model, I believe Steve's answer is helpful because it provides a starting point for solving the expression. Factoring the numerator is a common first step in solving rational expressions. From there, you can use polynomial long division or synthetic division to divide the numerator by the denominator.
I apologize if my response was not helpful to you. Is there anything else I can assist you with?
E. My math skills are a little rusty, so I think it would be best if you consult a calculator or a human for this one. But hey, why did the math book look sad? Because it had too many problems!
To solve this expression, you can use long division. Here's a step-by-step breakdown:
Step 1: Divide the first term of the numerator (-18x^3) by the first term of the denominator (3x). The result is -6x^2.
-6x^2 is the first term of the quotient.
-6x^2
_____________
3x + 2 | -18x^3 + 17x + 6
Step 2: Multiply the entire divisor (3x + 2) by -6x^2, which gives you -18x^3 - 12x^2.
-6x^2
_____________
3x + 2 | -18x^3 + 17x + 6
-18x^3 - 12x^2
Step 3: Subtract the previous result from the numerator. (-18x^3 + 17x + 6) - (-18x^3 - 12x^2) simplifies to 17x + 12x^2 + 6.
-6x^2 + 4x
_____________
3x + 2 | -18x^3 + 17x + 6
-18x^3 - 12x^2
__________________
17x + 12x^2 + 6
Step 4: Now we repeat the process by dividing the first term of the new polynomial (17x) by the first term of the divisor (3x), which gives you 12x.
12x is the next term of the quotient.
-6x^2 + 4x + 3
_____________
3x + 2 | -18x^3 + 17x + 6
-18x^3 - 12x^2
__________________
17x + 12x^2 + 6
17x + 12x^2 + 8
Step 5: Multiply the entire divisor (3x + 2) by 12x, which gives you 36x^2 + 24x.
-6x^2 + 4x + 3
_____________
3x + 2 | -18x^3 + 17x + 6
-18x^3 - 12x^2
__________________
17x + 12x^2 + 6
17x + 12x^2 + 8
__________________
-12x + 6
Step 6: Subtract the previous result from the new polynomial. (17x + 12x^2 + 8) - (-12x + 6) simplifies to 29x + 2.
-6x^2 + 4x + 3 + (29x + 2)/(3x + 2)
Since there are no more terms with a higher degree in the numerator than in the divisor, you have reached the end of the long division.
Therefore, the quotient is -6x^2 + 4x + 3, which corresponds to answer choice A.
well,
(-18x^3+17x+6) = -(3x+2)(6x^2-4x-3)
so, what do you think?