Question 183828This question is from textbook Algebra 2
: Given a polynomial and one of its factors, find the remaining factors of the polynomial. some factors may not be binomials.
PROBLEM:
(29) x^4+2x^3+2x^2-2x-3;x+1
Please help me with this question I have try time and time again and i just don't seem to know where to even begin. please help and thank you
This question is from textbook Algebra 2
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Given a polynomial and one of its factors, find the remaining factors of the polynomial. some factors may not be binomials.
PROBLEM:
(29) x^4+2x^3+2x^2-2x-3;x+1
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Use long division or synthetic division to divide the polynomial by x+1
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-1)....1....2....2....-2....-3
..........1..1....1.....-3..|..0
Quotient: x^3 + x^2 + x -3
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Since the coefficients of the quotient add up to zero, 1 is another zero:
1).....1..1....1.....-3
........1..2....3....|..0
Quotient: x^2 + 2 + 3
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Use the quadratic equation to find the remaining zeroes.
x = [-2 +- sqrt(4 - 4*1*3)]/2
x = [-2 +- sqrt(-8)]/2
x = [-2 +- 2isqrt(2)]/2
x = -1 + isqrt(2) or x = -1 -isqrt(2)
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All the zeroes: 1, -1 , -1 + isqrt(2) , x = -1 -isqrt(2)
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Cheers,
Stan H.
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