Chapter 5, Problem 2CV

Solution

To match : The vocabulary term with the description that best fits it.

1-D, 2-B, 3-C, 4-A.

Given information :

1. Conjugate Root Theorem 2. Fundamental Theorem of Algebra 3. Rational Root Theorem 4. Remainder Theorem

A. Determines $P\left(a\right)$ by dividing the polynomial by $x-a$ B. The degree equals the number of roots. C. Minimizes guessing fraction and integer solutions. D. Complex numbers as roots come in pairs.

Explanation :

Conjugate Root Theorem states that if a root of a polynomial is a complex number $a+bi$ , then its complex conjugate, $a-bi$ , is also a root which means theses roots come in pairs.

Fundamental Theorem of Algebra says that the degree of a polynomial equation tells you how many roots the equation will have which means if $P\left(x\right)$ is a polynomial of degree $n\ge 1$ , then $P\left(x\right)=0$ will have exactly $n$ roots and it includes multiple and complex roots.

Rational Root Theorem is used to find the rational solution of a polynomial equation. It states that if the coefficient of a polynomial is integers, it is easier to find all the possible rational roots by dividing each factor of the constant term by each factor of the leading coefficient.

Remainder theorem states that when a polynomial $P\left(a\right)$ is divided by the polynomial $\left(x-a\right)$ then the remainder is $f\left(a\right)$ .

So,

  

Therefore,

1-D, 2-B, 3-C, 4-A.