c(x) = 4x - 2
d(x) = x^2 + 5x
4x - 2(x^2 + 5x)
<em><u>Using FOIL, distribute each term appropriately. </u></em>
4x^3 + 20x^2 - 2x^2 - 10x
<em><u>Combine like terms.</u></em>
4x^3 + 18x^2 - 10x is the simplified polynomials achieved when c(x) and d(x) are multiplied.
Since 360 is a multiple of 120 then the answer is automatically 120. 120,240,360,480,600,720,840, and 960.
Answer:
15.8
Step-by-step explanation:
We are asked to find how many seconds it takes for an object to fall from a height of 4,000ft. We will use the given formula, t=h−−√4. Substituting h=4,000, we find
t=4000−−−−√4=15.8
So, the hammer reaches the river after 15.8 seconds.
Answer:
15+18
Step-by-step explanation:
3(5)+3(6)=15+18
Answer:
The factored expression is 2(x² + 5)(x + 3).
Step-by-step explanation:
Hey there!
We can use a factoring technique referred to as "grouping" to solve this problem.
Grouping is used for polynomials with four terms as a quick and easy factoring method to remove the GCF and get down to the initial terms that create the expression/function.
Grouping works in the following matter:
- Given equation: ax³ + bx² + cx + d
- Group a & b, c & d: (ax³ + bx²) + (cx + d)
- Pull GCFs and factors
Let's apply these steps to the given equation.
- Given equation: 2x³ + 6x² + 10x + 30
- Group a & b, c & d: (2x³ + 6x²) + (10x + 30)
- Pull GCFs and factors: 2x²(x + 3) + 10(x + 3)
As you'll see, we have a common term with both sides of the expression. This term, (x + 3), is a valuable asset to the factoring process. This is one of the factors for our expression.
Now, we use our GCFs to create another factor.
- List GCFs: 2x², 10
- Create a term: (2x² + 10)
Finally, we'll need to simplify this one by taking another GCF, 2.
- Pull GCF: 2(x² + 5)
Now that we have this term, we need to understand that this <em>could</em> also be factored further using imaginary numbers, but it is also acceptable to leave it in this form.
Therefore, we have our final factors: 2(x² + 5) and (x + 3).
However, when we factor, we place all of our terms together. This leaves us with the final answer: 2(x² + 5)(x + 3).
