Rewrite the given divisor into the general form x-a. Then, if all the terms of the dividend are present, you are ready to use synthetic division.
(x+3)(x−3)(x−4)
Practice makes perfect
To divide the given polynomials using synthetic division, all the terms of the dividend must be present. Since there are no missing terms, we do not need to rewrite the polynomial.
x^3 - 4x^2 - 9x + 36
Remember that the general form of the divisor in synthetic division is x-a. Therefore, we need to rewrite ours a little bit.
x+3 ⇔ x-(-3)
Now, we are ready to divide!
The quotient is a polynomial of degree 2 and the remainder is zero. We know that our remainder is correct because we were told that x+3 is a factor of the polynomial. Let's rewrite the given polynomial as the product of two factors.
( x^3 - 4x^2 - 9x + 36 ) = (x+3) ( x^2 - 7x + 12 )
Finally, let's factor the quadratic polynomial.
( x^3 - 4x^2 - 9x + 36 ) = (x+3)(x-3)(x-4)
