Which polynomial is equal to (-3x^2 + 2x - 3) subtracted from (x^3 - x^2 + 3x)?
<h3><u><em>
Answer:</em></u></h3>
The polynomial equal to (-3x^2 + 2x - 3) subtracted from (x^3 - x^2 + 3x) is 
<h3><u><em>Solution:</em></u></h3>
Given that two polynomials are: 
and 
We have to find the result when is subtracted from
In basic arithmetic operations,
when "a" is subtracted from "b" , the result is b - a
Similarly,
When is subtracted from , the result is:
Let us solve the above expression
<em><u>There are two simple rules to remember: </u></em>
- When you multiply a negative number by a positive number then the product is always negative.
- When you multiply two negative numbers or two positive numbers then the product is always positive.
So the above expression becomes:
Removing the brackets we get,
Combining the like terms,
Thus the resulting polynomial is found
Do you just wan't us to answer it or give you an explanation?
1. We use the recursive formula to make the table of values:
f(1) = 35
f(2) = f(1) + f(2-1) = f(1) + f(1) = 35 + 35 = 70
f(3) = f(1) + f(3-1) = f(1) + f(2) = 35 + 70 = 105
f(4) = f(1) + f(4-1) = f(1) + f(3) = 35 + 105 = 140
f(5) = f(1) + f(5-1) = f(1) + f(4) = 35 + 140 = 175
2. We observe that the pattern is that for each increase of n by 1, the value of f(n) increases by 35. The explicit equation would be that f(n) = 35n. This fits with the description that Bill saves up $35 each week, thus meaning that he adds $35 to the previous week's value.
3. Therefore, the value of f(40) = 35*40 = 1400. This is easier than having to calculate each value from f(1) up to f(39) individually. The answer of 1400 means that Bill will have saved up $1400 after 40 weeks.
4. For the sequence of 5, 6, 8, 11, 15, 20, 26, 33, 41...
The first-order differences between each pair of terms is: 1, 2, 3, 4, 5, 6, 7, 8...since these differences form a linear equation, this sequence can be expressed as a quadratic equation. Since quadratics are functions (they do not have repeating values of the x-coordinate), therefore, this sequence can also be considered a function.
5
-
15 would be in simplest form
