Asked by raechel
find the numerical values of the constants A, B and C such that 2x^3 +7x^2-x-6=(Ax+1)(x-1)(x+B)+4x-C
Answers
Answered by
Steve
well, just expand and equate coefficients:
2x^3 +7x^2-x-6 = Ax^3+(AB-A+1)x^2+(B+3-AB)x+(-B-C)
So, you have
A = 2
AB-A+1 = 7
B+3-AB = -1
-B-C = -6
A=2, so you have
2B-2+1=7, so B=4
That better work with
B+3-AB = -1
4+3-2*4 = -1 -- check
-B-C = -6
-4-C = -6
C=2
2x^3 +7x^2-x-6 = Ax^3+(AB-A+1)x^2+(B+3-AB)x+(-B-C)
So, you have
A = 2
AB-A+1 = 7
B+3-AB = -1
-B-C = -6
A=2, so you have
2B-2+1=7, so B=4
That better work with
B+3-AB = -1
4+3-2*4 = -1 -- check
-B-C = -6
-4-C = -6
C=2
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.