F(t)=3t^2+3t, Find f(7)
2 answers:
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Answer:
2n³ - 3n² - 7n + 3
Step-by-step explanation:
Hi there! Don't worry, polynomials seem hard but you will get them with practice.
I am going to show you 2 methods of multiplying polynomials. These methods are universal, or they work with any polynomial multiplication problem:
<h2>Method 1: Distributive Property</h2>This is perhaps the most common method. You distribute 1 value to another or multiply each and every single term.
Let's solve it!
- (n² - 3n + 1)(2n + 3)
- n²(2n + 3) - 3n(2n + 3) + 1(2n + 3)
- n²(2n) + n²(3) - 3n(2n) - 3n(3) + 2n + 3 See how I distributed the values?
- 2n³ + 3n² - 6n² - 9n + 2n + 3
Now, we add up like terms. Like terms should have the same coefficient and should be raised to the same power.
- 2n³ + 3n² - 6n² - 9n + 2n + 3
- 2n³ - 3n² - 7n + 3
There you have it! This is how you solve with The distributive Property Method.
<h2>Method 2: Area Model</h2>This is the next universal method, Area modeling.
Area models can be set up by the number of terms we have. In the first polynomial we have three terms:
- n²
- -3n
- +1
Just for this method, keeping the positive signs helps.
For the binomial, we have two terms (hence, binomial)
- 2n
- +3
We set up our are model like this, with the terms laid out as side lengths of a rectangle. (Attachment "A")
Next, we find the area of each individual tile. (Attachment "B")
Now, we add like terms. Something nice about area models is that most of the time, the like terms are matched up in a diagonal. (Attachment "C")
- 2n³ + 3n² - 6n² - 9n + 2n + 3
- 2n³ - 3n² - 7n + 3
We end up with the same answer as before.
-Chetan K
