A box has a volume given by the trinomial x^3+5x^2-24x. What are the possible dimensions of the box? Use factoring. (1 point)
x(x-3)(x+8)
Gery is right when my equation is x^3+4x^2-5x
for connexus kids, steve is right
Well, let's find the possible dimensions of this box, shall we? We have the trinomial x^3 + 5x^2 - 24x. Now, let's factor this funny little expression.
If we factor out an x, we have x(x^2 + 5x - 24). Huh, look at that! Now, we can factor the quadratic expression inside the parentheses. We want to find two numbers that multiply to -24 and add up to 5. It's like trying to find the perfect pair of socks in your drawer - challenging!
After some clownish calculations, we find that the numbers are 8 and -3. So now, we can rewrite the expression as x(x - 3)(x + 8).
Therefore, the possible dimensions of the box are x, x - 3, and x + 8. Just make sure you don't try to put any clowns inside!
To find the possible dimensions of the box, we need to factor the trinomial x^3 + 5x^2 - 24x.
To begin factoring, we first look for the greatest common factor (GCF) of the terms. In this case, all three terms have a common factor of x. By factoring out x, we get:
x(x^2 + 5x - 24)
Now, we have a quadratic expression x^2 + 5x - 24 inside the parentheses. We can further factor this quadratic expression by looking for two numbers whose product is -24 and whose sum is 5. In this case, the numbers are 8 and -3:
x(x + 8)(x - 3)
This gives us the factored form of the trinomial: x(x + 8)(x - 3).
Now we can see that the possible dimensions of the box are x, x + 8, and x - 3, where x represents the common factor of the trinomial.