Solving a cubic

To solve a cubic, a factor must be given or determined.
Then the equation is divided by polynomial division by the factor.
The answer will be a quadratic and the remaindor 0.
Solve the quadratic for the other 2 answers.

Remember a factor or a root or divisible means remaindor is 0.
Use Remaindor Theorem to verify the remaindor is 0.
If first factor has to be determined, try (x - 1) or (x + 1) or (x - 2) or (x +2) for remaindor of 0.

p(x) = x³ – 7x – 6, and let's divide by the linear factor x – 4 (so a = 4): So we get a quotient of q(x) = x² + 4x + 9 on top, with a remainder of r(x) = 30

1. Show that 2x³ + x² -13x + 6 is divisible by x-2. Hence solve the equation.
2. Find the value of the constant k such that (x + 1) is a factor of the expression  2x³ + 7x² + kx - 3. For this value of k solve the equation  2x³ + 7x² + kx - 3.
3. f(x) = x³ + ax² + bx + 6 The remainder when f(x) is divided by x + 1 and x - 2 are 20 and 8 respectively, find the values of a and b. Hence solve the equation f(x) = 0