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