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Question 47631: Hi i was wandering if you could please answer the following question on factorising cubic polynomails using long division:
4x^3+35x^2+84x+45
The answer in the back of the book for that question was (4x+3)(x+3)(x+5)
I can factor cubic polynomials using long divsion when they don't have a number in front of x^3, e.g x^3+35x^2=84x+45. But i can't do the cubic polynomials with a number infront of x^3.
I would be grateful if you could please help
Thankyou
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 4x^3+35x^2+84x+45
The answer in the back of the book for that question was (4x+3)(x+3)(x+5)
If that is the answer in the back of the book the algebraic expression
is 4x^3=35x^2+24x+45 and not what you posted.
Now, how do you go about factoring it?
That depends on what you have learned up to this point in you study
of algebra.
1st You might graph it if you have a graphing calculator.
2nd You might know that if "p/q" is a zero of the expression
then p is a factor of 45 and q is a factor of 4. Then if
p/q is a zero one of the factors of the expression is (qx-p).
If you know these things you should be able to factor expressions
of this kind that have rational zeroes.
Cheers,
Stan H.
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