The factor of the polynomial, the area of the pool and the simplified expression are all algebraic expressions
How to simplify the expressions?
Factor of the polynomial
The polynomial is given as:
2x^3 + 6x^2 + 6x + 18
Factor out 2
2x^3 + 6x^2 + 6x + 18 = 2(x^3 + 3x^2 + 3x + 9)
Factorize
2x^3 + 6x^2 + 6x + 18 = 2(x^2(x + 3) + 3(x + 3))
Factor out x + 3
2x^3 + 6x^2 + 6x + 18 = 2(x^2 + 3)(x + 3)
Expand
2x^3 + 6x^2 + 6x + 18 = (2x^2 + 6)(x + 3)
Hence, 2x^2 + 6 is a factor of the polynomial 2x^3 + 6x^2 + 6x + 18
The length of the pool
The given parameters are:
Area = 2x^3 - 29x + 12
Width = x + 4
The length is calculated as:
Length = Area/Width
This gives
Length = 2x^2 - 29x + 12/x + 4
Factorize the numerator
Length = (2x^2 - 8x + 3)(x + 4)/x + 4
Cancel out x + 4
Length = 2x^2 - 8x + 3
Hence, the length of the pool is 2x^2 - 8x + 3
Simplify the expression
The expression is given as:
(3s^2 - 2s + 1) [tex]\div[/tex] (s^2 - s + 2)
Evaluate the quotient
3 + (s - 5)/(s^2 - 5 + 2)
Hence, the simplified expression is 3 + (s - 5)/(s^2 - 5 + 2)
Read more about algebraic expressions at:
https://brainly.com/question/2164351
