Synthetic Division and Rational Root Theorem

This video tutorial covers polynomial test review, focusing on synthetic and long division methods. It explains Descartes' Rule of Signs and demonstrates finding zeros using the rational root theorem. The tutorial provides step-by-step examples to help students understand polynomial division and root finding techniques.

What is the first step in synthetic division?

• Set the divisor equal to zero to find the root.

• Multiply the coefficients directly.

• Add the coefficients together.

• Divide the coefficients by the divisor.

In synthetic division, what do you do after bringing down the first coefficient?

• Ignore it and move to the next step.

• Subtract it from the next coefficient.

• Divide it by the root.

• Multiply it by the root and add to the next coefficient.

What is the result of synthetic division when the remainder is zero?

• The polynomial has no real roots.

• The divisor is a factor of the polynomial.

• The divisor is not a factor of the polynomial.

• The polynomial is prime.

What is the main difference between synthetic and long division?

• Synthetic division is faster and simpler for linear divisors.

• Long division is only for quadratic divisors.

• Long division is faster than synthetic division.

• Synthetic division can only be used for polynomials with even degrees.

In long division, what do you do after multiplying the divisor by the current term?

• Divide the result by the next term.

• Multiply the result by the next term.

• Add the result to the current dividend.

• Subtract the result from the current dividend.

What does Descartes' Rule of Signs help determine?

• The number of positive and negative real zeros.

• The leading coefficient of the polynomial.

• The degree of the polynomial.

• The constant term of the polynomial.

How do you apply Descartes' Rule of Signs to find negative real zeros?

• Replace x with -x and count sign changes.

• Count the number of terms in the polynomial.

• Divide the polynomial by x.

• Multiply all coefficients by -1.

What is the Rational Root Theorem used for?

• Calculating the derivative of a polynomial.

• Finding the integral of a polynomial.

• Finding possible rational zeros of a polynomial.

• Determining the degree of a polynomial.

According to the Rational Root Theorem, what are potential rational roots?

• Factors of the constant term divided by factors of the leading coefficient.

• Factors of the leading coefficient divided by factors of the constant term.

• The sum of the coefficients.

• The product of the coefficients.

What is the next step after finding a potential root using the Rational Root Theorem?

• Multiply it by the polynomial.

• Ignore it and try another root.

• Use synthetic division to verify if it is a root.

• Add it to the polynomial.