How Do You Factor A Cubic Polynomial?
• Let the expression be in the form of aX3+bX2+cX+d • Find the factors of d (the numbers that d is divisible by): • Example: the factors of 8 are 1,-1,2,-2,4,-4,8,-8 • Substitute by each factor in the polynomial to determine the factors that makes the polynomial equal to zero. • If the factor that made the polynomial equal zero is (a) then (X-a)is a factor of the polynomial (The polynomial is divisible by it) • Continue to substitute by the factors of the free term until you get all the factors of the polynomial or you can divide the main polynomial by the only factor that you got (X-a) by using the long division: • Example : X3-6X2+11x-6 If we substitute by 1,2,3 (the positive factors of the free term) the expression equals zero, then (X-1),(X-2),(X-3) are the factors of the polynomial.
