The cubic polynomial f(x)=3x^3–20x^2+cx+60 has a factor (x–3). Find the value of the constant c. With this value of c, Express the polynomial as the product of three linear factors

Answer 1

There are a number of ways to solve this---here's one:

Do the long division---when you get to the term with the c in it, it will become obvious what c needs to be so the division has no remainder. At that point, you'll be left with quadratic---to be solved by the normal methods

Answer 2

Since (x-3) is a factor of f(x), f(3)=0 according to remainder theorem.

:. f(3)=3(27)-(20)(9)+c(3)+60=0

:. -39+3c=0

:. c=13.

Now dividing f(x) by (x-3), we get:

(3x^3-20x^2+13x+60)/(x-3) = 3x^2-11x-20 = (x-5)(3x-4)

Hence f(x)=(x-3)(x-5)(3x-4)