Finding Near Squares Using Polynomial Identities

This video tutorial explains how to find the near square of a number using polynomial identities. It begins with an introduction to polynomial identities and their properties, followed by a demonstration of multiplying polynomial expressions. The concept of near squares is introduced, showing their relation to perfect squares. The tutorial then applies polynomial identities to find near squares, providing examples to illustrate the process. By the end, viewers will understand how to use polynomial identities to determine near squares and rearrange squares into rectangles.

What is a polynomial identity?

• An equation that is true only for positive values

• An equation that is never true

• An equation that is true for all values of the variable

• An equation that is true for some values of the variable

Which of the following represents the identity (X + y)(X - y)?

• X^2 + 2xy + y^2

• X^2 - y^2

• X^2 + y^2

• X^2 - 2xy + y^2

How can the expression 3^2 - 1^2 be factored using polynomial identities?

• (3 - 1)(3 - 1)

• (3 + 1)(3 + 1)

• (3 + 2)(3 - 2)

• (3 + 1)(3 - 1)

What is the near square of 144 using polynomial identities?

• 143

• 146

• 142

• 145

If you have a perfect square of 144, how many tiles would you have on one side after removing one tile?

• 11

• 14

• 13

• 12

What is the near square of 1024 using polynomial identities?

• 1022

• 1023

• 1026

• 1025

To make a rectangle as near a square as possible with 1023 tiles, what should be the dimensions?

• 32 by 32

• 33 by 31

• 31 by 31

• 34 by 30