Question

answer the following questions.
(1) choose the best answer.
to find the roots of a polynomial, it is often useful to find the ____ of the polynomial.

• powers
• coefficients
• factors
• solutions

(2) choose the best answer.
roots of a polynomial are the values that make the polynomial equal to ____.

• one
• zero
• ( x )
• negative one

(3) choose the best answer.
____ number roots of a polynomial are the points where the graph of the related polynomial function crosses the ( x )-axis.

• imaginary
• even
• odd
• real

(4) choose the best answer.
if ( abc = 0 ), then ____.

• ( a = 0 )
• ( a = 0 ) and ( b = 0 ) and ( c = 0 )
• ( a = 0 ) or ( b = 0 ) or ( c = 0 )
• ( b = 0 )

Explanation:

1. Factoring a polynomial allows us to use the zero product property to find its roots, as each factor set to zero gives a root.
2. By definition, roots (or zeros) of a polynomial are the input values that result in the polynomial evaluating to 0.
3. Imaginary roots do not appear on a real-number coordinate plane; only real roots correspond to where the polynomial graph crosses the $x$-axis.
4. The zero product property states that if a product of terms equals 0, at least one of the terms must be 0.

Answer:

1. C. factors
2. B. zero
3. D. Real
4. C. $a = 0$ OR $b = 0$ OR $c = 0$