Given a factor or zero find all the remaining zeros

What is the first step in finding all zeros of a polynomial?

• Graph the polynomial

• Apply synthetic or long division

• Guess the zeros

• Use the quadratic formula

When using synthetic division, what must be true about the remainder?

• It should be zero

• It should be less than zero

• It should be greater than zero

• It should be equal to the divisor

What is the purpose of using the quadratic formula in polynomial factorization?

• To simplify the polynomial

• To determine the leading coefficient

• To find the degree of the polynomial

• To find zeros that cannot be factored easily

How can you factor a polynomial with four terms?

• By using the quadratic formula

• By multiplying all terms

• By grouping terms and factoring common factors

• By using synthetic division

What is a complex conjugate in the context of polynomial zeros?

• A pair of complex numbers with opposite imaginary parts

• A pair of real numbers

• A pair of irrational numbers

• A single complex number

Why might long division be preferred over synthetic division for complex numbers?

• It requires fewer steps

• It is more intuitive

• It avoids arithmetic mistakes

• It is faster

What is the result of multiplying two complex conjugates?

• An irrational number

• A polynomial

• A complex number

• A real number

What should you do if a polynomial is not factorable by simple methods?

• Guess the factors

• Use the quadratic formula

• Ignore the polynomial

• Use a calculator

What is the benefit of knowing two zeros of a polynomial?

• It allows for immediate graphing

• It helps in using synthetic division effectively

• It simplifies the polynomial

• It eliminates the need for further calculations

What is the significance of the fundamental theorem of algebra in this context?

• It determines the degree of the polynomial

• It ensures the polynomial has as many zeros as its degree

• It simplifies the polynomial

• It provides a method for factoring