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Question 449130: Can you please factorise the following:
x^4 + 6x^3 + 8x^2 -6x + -9
x-1 is a factor.
i did, using long division divide polynomial by x-1 and i got x^3+7x^2+15x+9
so my factors are (x-1)(x^3+7x^2+15x+9)
now how can i factorise that further, do i i have to use long division or is there a quicker way?
thanks
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Can you please factorise the following:
x^4 + 6x^3 + 8x^2 -6x + -9
x-1 is a factor.
i did, using long division divide polynomial by x-1 and i got x^3+7x^2+15x+9
so my factors are (x-1)(x^3+7x^2+15x+9)
now how can i factorise that further, do i have to use long division or is there a quicker way?
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Look at the coefficients of the original problem.
The sum of the coefficients is 1+6+8-6-9 = 0
That means that x = 1 is a root; so x-1 is a factor.
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Now look at x^3+7x^2+14x+9
The sum of those coefficients is not zero, so x-1 is not a factor.
But f(-1) = -1+7-15+9 = 0; so x = -1 is a zero, so x+1 is a factor.
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You have found two of the roots and can find the remaining roots
using the Quadratic formula.
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The fastest ways to find the Real Roots is to graph
the problem with a graphing calculator. The find
the intersection of the problem with y = 0 to
find the Real roots. Remember: if "a" is a root, x-a is a factor.
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Cheers,
Stan H.
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