I need some help with this question. Is there someone can help me?

Question

A rectangular kitchen rug has a length of 5 x ³ + 4 x and a width of 6 x ² – 2 x + 7. What is the area of the rug in simplest form?

Answer 1

Area = LW = (5x^3+ 4x)(6x^2-2x+7) = 5x^5 -10x^4+14x^3 -8x^2 +28x

that's simplest in some sense

or

factor it further into more simple factors

x(5x^2+ 4)(6x^2-2x+7) if you look at the discriminants, you can see it can't be factored further

discriminant = b^2 - 4ac is negative if there are no further factors

if x=0 A=0

if x=1 A= 99

if x=2 A= 1296

if x=3 Area spreads faster than covid19 viruses on steroids

the area grows exponentially (literally & figuratively) as x increases

Answer 2

Hi Luisa,

Given Length = 5 x ³ + 4 x

Width = 6 x ² – 2 x + 7

Area of Rectangle = Length * Width =

A = ( 5 x ³ + 4 x ) ( 6 x ² – 2 x + 7)

= 30 X⁵ - 10 X⁴ + 35 X³ +24 X ³ - 8 X² + 28 X

= 30 X⁵ - 10 X ⁴ + 59 X³ -8 X² +28 X

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