Please Help! How do I work this?
The Volume of the box is represented by (x^2+5+6)(x+5). Find the polynomial that represents the area of the bottom of the box.
The area must have the dimensions of (length)^2, so the answer must be
(x^2+5+6)
Souldn't there be an "x" after the 5?
To find the polynomial that represents the area of the bottom of the box, we need to factor the given expression for the volume.
The given expression for the volume is (x^2 + 5x + 6)(x + 5).
To factor this expression, we can look for common factors and use the distributive property.
The expression can be rewritten as follows:
(x + 2)(x + 3)(x + 5)
Here's how we factored the expression:
1. Split the middle term, 5x, into two terms whose coefficients multiply to give 6 and whose sum is 5. In this case, the two numbers are 2 and 3, since 2 * 3 = 6 and 2 + 3 = 5.
2. Use the grouping method to factor the expression. Group the terms as follows:
(x^2 + 2x) + (3x + 5)
3. Factor out the common factors from each group:
x(x + 2) + 3(x + 2)
4. Notice that both terms have (x + 2) as a common factor. Factor out the common factor:
(x + 2)(x + 3)
Therefore, the polynomial that represents the area of the bottom of the box is (x + 2)(x + 3).