1. ## Polynomials

The polynomial p(x)=x^3+mx^2+nx-56 is exaclty divisible by x-7 and x+2.

a) Find the values of m and n

b) Find the third factor

c) Sketch

How do I do this? I have no idea...

2. Originally Posted by Unwelcome
The polynomial p(x)=x^3+mx^2+nx-56 is exaclty divisible by x-7 and x+2.
If they both divide in evenly (and since they don't contain factors of each other), then their product, x^2 - 5x - 14, must also be a factor of x^3 + mx^2 + nx - 56.

Obviously, the remaining factor of the cubic must be linear, and clearly the leading coefficient of that factor must be "1". So the remaining factor is of the form "x + a".

Since the constant of the known factor is -14 and the constant of the original polynomial is -56, then you must have (-56)/(-14) = 4, so the remaining factor must be "x + 4".

Multiply the known factor by the remaining factor, and see what you get for "m" and "n". Sketch the result.