Presenting the Rational Zero Theorem (4.5.1)

Question 1

• A rational number is a fraction. An irrational number is a radical or imaginary number that cannot be written as a fraction.

Answer 1

• A rational number is a fraction. An irrational number is a radical or imaginary number that cannot be written as a fraction.

Question 2

• If the polynomial has integer coefficients, then every rational zero of f has the form where p and q have no common factors other than 1, p is a factor of a0, and q is a factor of an. (The factors of a0 and an include all positive and negative factors.)

Answer 2

• If the polynomial has integer coefficients, then every rational zero of f has the form where p and q have no common factors other than 1, p is a factor of a0, and q is a factor of an. (The factors of a0 and an include all positive and negative factors.)

Question 3

• The rational zero theorem says that every rational zero for a function takes the form of a fraction with the numerator being a factor of the constant that ends the function and the denominator being a factor of the coefficient of the highest power in the function.

Answer 3

• The rational zero theorem says that every rational zero for a function takes the form of a fraction with the numerator being a factor of the constant that ends the function and the denominator being a factor of the coefficient of the highest power in the function.

Question 4

• To find all rational zeros, make a list of the factors of the final constant and the beginning coefficient. Combine these factors in all unique possibilities with the constant’s factors in the numerator and the coefficient’s factors in the denominator. Substitute each of these into the function, and each one that yields f (x) = 0 is a rational zero.

Answer 4

• To find all rational zeros, make a list of the factors of the final constant and the beginning coefficient. Combine these factors in all unique possibilities with the constant’s factors in the numerator and the coefficient’s factors in the denominator. Substitute each of these into the function, and each one that yields f (x) = 0 is a rational zero.