Answer:
The area of rectangle is [tex]2x^4 + x^3 -15x^2 +8x +24[/tex].
Step-by-step explanation:
Given that,
Length of rectangle = [tex]2x^3-5x^2+8[/tex]
Width of rectangle = [tex]x + 3[/tex]
Area of rectangle = A = ?
Area of a rectangle is calculated by multiplying length with width
A = l * w
In our case
[tex]l = 2x^3-5x^2+8[/tex]
[tex]w = x + 3[/tex]
[tex]A = l * w[/tex]
=> [tex](2x^3-5x^2+8)*(x+3)[/tex]
=> [tex]x*(2x^3-5x^2+8) +3(2x^3-5x^2+8)[/tex]
=> [tex](2x^4-5x^3+8x) +(6x^3-15x^2+24)[/tex]
=> [tex](2x^4) + (-5x^3+6x^3) + (-15x^2) +(8x) +(24)[/tex]
=> [tex](2x^4) + (x^3) + (-15x^2) +(8x) +(24)[/tex]
=> [tex]2x^4 + x^3 -15x^2 +8x +24[/tex]
Therefore, the area of rectangle is [tex]2x^4 + x^3 -15x^2 +8x +24[/tex].
