Factors of Polynomials

You will be able to

• Use the remainder theorem to find the remainder when a polynomial is divided by (x − r) or (px − q).
• Use the factor theorem to show that a linear expression is, or is not, a factor of a polynomial.
• Find an unknown coefficient in a polynomial from a given remainder or a given factor.

You will be able to

• Find a linear factor of a cubic by testing candidate values with the factor theorem.
• Divide a cubic by a linear factor, by long division or by comparing coefficients, to find the quadratic quotient.
• Solve a cubic equation completely, giving the roots exactly (as fractions or surds) where required.