The rectangle below has an area of 6n^4+20n^3+14n^26n 4 +20n 3 +14n 2 6, n, start superscript, 4, end superscript, plus, 20, n, cubed, plus, 14, n, squared.The width of the rectangle is equal to the greatest common monomial factor of 6n^4, 20n^3,6n 4 ,20n 3 ,6, n, start superscript, 4, end superscript, comma, 20, n, cubed, comma and 14n^214n 2 14, n, squared.What is the length and width of the rectangle?
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Width of Rectangle = 2n² & Length of Rectangle = 3n² + 10n + 7
Step-by-step explanation:
Area of Rectangle =6n⁴ + 20n³ + 14n²
= 2n² ( 3n² + 10n + 7)
= 2n² (3n² + 3n + 7n + 7)
= 2n² (3n(n + 1) + 7(n+1))
= 2n² (n+1)(3n + 7)
Width of the rectangle is equal to the greatest common monomial factor of 6n⁴, 20n³ & 14n²
6n⁴ = 2n² * 3n²
20n³ = 2n² * 10n
14n² = 2n² * 7n
greatest common monomial factor = 2n²
Width of Rectangle = 2n²
Length of Rectangle = 2n² (n+1)(3n + 7) /2n²
= (n+1)(3n + 7)
= 3n² + 10n + 7
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