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I did this question 3 times seperately, each time I made the same mistake. (3)^3 = 27 as you state in the first line, I put down 9 each time!!!
Since f(3)=0, 27+9a+3b+c=0,...(1)
so if f(3) = 0 and f(-2) = -40, what are the values of a and b? I've been bearing in mind that c = 0 to work this out but I always end up with fractions in my answer, the book says a and b are integers.
The factor theorem states that a polynomial f(x) is divisible by (x-a) if f(a)=0.
Since it is divisible by x,
it follows that f(x)=0, therefore, the given polynomial is equal to zero, and c=0. True, because, if c is a non-zero constant, the polynomial is not divisible by x.
I have an expression: f(x) = x^3 + ax^2 + bx + c which is divisable by x. Does this mean that