Answer:
V = x³ + 3x² + 3x + 1 in³
Step-by-step explanation:
The volume (V) of a cube is calculated as
V = s³ ( where s is the side ) , then
V = (x + 1)³
= (x + 1)(x + 1)(x + 1) ← expand second pair using FOIL
= (x + 1)(x² + 2x + 1) ← distribute
= x³ + 2x² + x + x² + 2x + 1 ← collect like terms
= x³ + 3x² + 3x + 1
Problem # 1
Not Factored: (5x^2 - 13x - 6)
Factored: (5x + 2 )(x - 3)
There is no real "work" to be shown for this, you can see that
1) Seperating 5x^2 into 5x and x will get you the equation in the form:
(5x ) (x ) = 5x^2 +
2) To complete this factor you need to guess which two numbers will add together to give you - 13x and multiply to form -6 (from the original unfactored equation). The numbers that will do this are 2 and 3
3) You can plug in negative or positives of those numbers to make sure they give you the exact results you need.
For example testing -2 and 3 you will get: (5x - 2) (x + 3 ) = 5(x^2) - 2x + 15x - 6 = 5x^2 +13x - 6. This is NOT the same as the unfactored equation. So you know -2 and 3 is the wrong choice. Choosing 2 and -3 will give you the answer instead.
As i said, there's no actual "work" to show this, you have to make guesses and try to factor it.
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Problem # 2
Not Factored: 4x^4 - 28x^3 + 48x^2
Factored: 4x^2 (x^2 - 7x + 12) =
4x^2 (x - 3) (x - 4)
To solve this, you factor out the 4x^2 from the entire equation. Then you can further factor the quadratic equation by seperating x^2 into (x )(x ) and guessing for which numbers will add to -7x and multiply to 12
Answer:
D. 5x - 1
Step-by-step explanation:
(f+g)(x) ➡ f(x) + g(x)
3x -2 + 2x + 1 = 5x -1
