Given One Factor Find All of the Remaining Factors Using Synthetic Division

The video tutorial explains synthetic division of polynomials, starting with setting up the division problem and applying synthetic division to find the quotient and remainder. It then interprets the results, showing how to factor the quadratic term using the difference of squares method. The tutorial concludes with a summary and homework assignment to find all linear factors of a polynomial.

What is the first step in synthetic division when dividing a polynomial by a binomial?

• Subtract the divisor from the polynomial

• Set the divisor equal to zero and solve for X

• Multiply the coefficients

• Add the coefficients

In synthetic division, what do you do with the coefficients of the polynomial?

• Add them together

• Multiply them by the divisor

• Use them in the division process

• Ignore them

What does a remainder of zero indicate in synthetic division?

• The divisor is a factor

• The polynomial cannot be divided

• The divisor is not a factor

• The polynomial is prime

What is the form called when factoring X^2 - 4?

• Sum of cubes

• Quadratic formula

• Difference of squares

• Perfect square trinomial

After factoring X^2 - 4, what are the linear factors?

• X + 3 and X - 3

• X + 2 and X - 2

• X + 4 and X - 4

• X + 1 and X - 1