Chapter 4.5, Problem 70E

To determine

To find the greatest common factor of $44x^3,24x^2$ .

Answer to Problem 70E

  $4x^2$

Explanation of Solution

Given information: $44x^3,24x^2$

Formula Used: To find the greatest common factor of two or more algebraic expressions, find the greatest common factors of the numbers and the variables separately. After finding the two, multiply them, to reach the greatest common factors of the expressions combines.

Calculation:

Given, $44x^3,24x^2$

First, the greatest common factors of 44 and 24 are evaluated

Factors of $44=1,2,4,22,44$

Factors of $24=1,2,3,4,6,8,12,24$

Highest common factor of 44 and 24 $=4$

Second, the greatest common factor of $x^3\&x^2$

Factors of $x^3=x\times x\times x$

Factors of $x^2=x\times x$

Greatest common factor of $x^3\&x^2=x\times x$

  $=x^2$

Hence, the greatest common factor of the two algebraic expressions

  $=4\times x^2$

  $=4x^2$ This is the greatest common factor.