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Question
Hello, I am really stuck on this problem.

I have the polynomial P(x) = 7x^3+8x^2-3x+8

I am told to use synthetic division to find the value of P(7).

I'm normally really good at synthetic division/polynomials, but this one is really tripping me up. First, I know I need to use synthetic division (which gave me a result of 7x^2+57x+396+2780/(x-7)), then I was told I have to factor the result to find the roots, but I am having trouble factoring that. The answer shouldn't have any remainder afterwards.

If you could please show me the answer, as what as what steps you are taking so I can hopefully find what I am doing wrong, it would be much appreciated. Thanks, John

You don't use synthetic division to find P(7).  You just substitute 7 for x to get
P(7) = 7(7^3) +8(7^2) -3(7) +8 = 2780
If Y is a factor then p(Y) = 0.
You can't factor this expression.
You can look at it and see that Y would have to be negative.
P(-1) = 12 and P(-2) = -10 and so there's a root between -1 and -2.

Algebra

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