SOLUTION: x−2) is a factor of 2x³+ax²+bx−2,and when this expression is divided by (x−3)the remainder is-50. Find a and b and the remaining factors a)x³-5x²-x+5,(b) x³-9x²+27x+1

Algebra ->  Square-cubic-other-roots -> SOLUTION: x−2) is a factor of 2x³+ax²+bx−2,and when this expression is divided by (x−3)the remainder is-50. Find a and b and the remaining factors a)x³-5x²-x+5,(b) x³-9x²+27x+1      Log On


   

Question 1176598: x−2) is a factor of 2x³+ax²+bx−2,and when this expression is divided by (x−3)the remainder is-50.
Find a and b and the remaining factors
a)x³-5x²-x+5,(b) x³-9x²+27x+18,(c) 2x³+x²-18x+5.State the roots of the equation 2x³+ax²+bx-2=0
Answer by greenestamps(13367) About Me  (Show Source):
You can put this solution on YOUR website!


Call the expression p%28x%29+=+2x%5E3%2Bax%5E2%2Bbx-2.

(x-2) being a factor of p(x) means that the remainder when p(x) is divided by (x-2) the remainder is 0; that means

p%282%29+=+2%282%5E3%29%2Ba%282%5E2%29%2Bb%282%29-2=0
16%2B4a%2B2b-2=0
4a%2B2b=-14
2a%2Bb+=+-7 [1]

Similarly, if p(x) divided by (x-3) leaves remainder -50, that means

p%283%29+=+2%283%5E3%29%2Ba%283%5E2%29%2Bb%283%29-2+=+-50

54%2B9a%2B3b-2+=+-50
9a%2B3b+=+-102
3a%2Bb+=+-34 [2]

Solve equations [1] and [2] to find a=-27 and b=47.

The expression is 2x^3-27x^2+47x-2.

We know one of the roots is 2; synthetic division leads us to

2x%5E3-27x%5E2%2B47x-2+=+%28x-2%29%282x%5E2-23x%2B1%29

The quadratic factor has irrational roots; you can find them exactly using the quadratic formula; or you can find them approximately using a graphing calculator or similar tool.

I'm guessing the a), b), and c) in your post are supposed to be the answer choices; but none of them is correct....