Question

PLEASE HELP PRE CAL!!

Answer 1

Answer:

Width = 2x²

Length = 7x² + 3

Step-by-step explanation:

∵ The area of a rectangle is $14x^{4}+6x^{2}$

∵ Its width is the greatest common monomial factor of $14x^{4}$ and 6x²

- Let us find the greatest common factor of 14 , 6 and $x^{4}$ , x²

∵ The factors of 14 are 1, 2, 7, 14

∵ The factors of 6 are 1, 2, 3, 6

∵ The common factors of 14 and 6 are 1, 2

∵ The greatest one is 2

∴ The greatest common factor of 14 and 6 is 2

- The greatest common factor of monomials is the variable with

   the smallest power

∴ The greatest common factor of $x^{4}$ and  x² is x²

∴ The greatest common monomial factor of  $14x^{4}$ and 6x² is 2x²

∴ The width of the rectangle is 2x²

To find the length divide the area by the width

∵ The area = $14x^{4}+6x^{2}$

∵ The width = 2x²

∴ The length = ( $14x^{4}+6x^{2}$) ÷ (2x²)

∵  $14x^{4}$ ÷ 2x² = 7x²

∵ 6x² ÷ 2x² = 3

∴ ( $14x^{4}+6x^{2}$) ÷ (2x²) = 7x² + 3

∴ The length of the rectangle is 7x² + 3