Given One Zero or Factor Find the Remaining Zeros

The video tutorial explains how to find zeros of a polynomial when given its factors. It begins by discussing the relationship between factors and zeros, followed by a demonstration of synthetic division to find zeros. The tutorial continues with finding remaining factors using synthetic division and factoring a quadratic expression. Finally, it concludes with a summary of the solution set of the polynomial.

What is the relationship between factors and zeros in a polynomial?

• Factors are the coefficients of the polynomial.

• Factors are the solutions to the polynomial equation.

• Zeros are the values that make the polynomial equal to zero.

• Zeros are the exponents in the polynomial.

Which method is preferred for dividing polynomials when given factors?

• Long division

• Synthetic division

• Graphical method

• Trial and error

What is the first step in synthetic division?

• List the coefficients

• Multiply the factors

• Find the remainder

• Set up the division table

How do you determine additional zeros from a polynomial using synthetic division?

• By dividing the polynomial by a known factor

• By multiplying the coefficients

• By subtracting the remainder

• By adding the factors

What is the purpose of factoring a quadratic expression in the context of polynomials?

• To simplify the polynomial

• To find the remaining zeros

• To increase the degree of the polynomial

• To change the polynomial's coefficients

Which of the following is a valid factorization of 8X^2 + 2X - 3?

• (8X - 1)(X + 3)

• (4X + 3)(2X - 1)

• (8X + 3)(X - 1)

• (4X - 1)(2X + 3)

What is the zero product property used for in polynomial factorization?

• To calculate the remainder

• To find the zeros of the polynomial

• To determine the leading coefficient

• To find the degree of the polynomial