Chapter 11, Problem 1VR

Complete each statement with the correct term from the column on the right. Some of the choices may be used more than once or not at all.

common

similar

product

difference

factor

factorization

grouping

monomial

binomial

trinomial

zero

To _________a polynomial is to express it as a product. [11.1a]

To determine

To fill: The blanks for the statement “To_______ a polynomial is to express it as a product.” from the provided choices.

Answer to Problem 1VR

Solution:

To factor a polynomial is to express it as a product.

Explanation of Solution

Given Information:

The provided choices are as follows,

1: Common

2: Similar

3: Product

4: Difference

5: Factor

6: Factorization

7: Grouping

8: Monomial

9: Binomial

10: Trinomial

11: Zero

Explanation:

Consider a polynomial.

By definition, expressing the polynomial in the form of product of two or more polynomials of lower degree is called factoring.

Thus, to factor a polynomial is to express the polynomial as a product.

For example:

$f\left(x\right)=x^2+4x+4$

Rewrite the polynomial as,

$\begin{array}{c}f\left(x\right)=x^2+4x+4\\ =x^2+2x+2x+4\\ =x\left(x+2\right)+2\left(x+2\right)\\ =\left(x+2\right)\left(x+2\right)\end{array}$

This procedure to rewrite the polynomial $f\left(x\right)=x^2+4x+4$ as $f\left(x\right)=\left(x+2\right)\left(x+2\right)$ is called factoring.