Simplify the expression below. Then classify the resulting expression
2 answers:
Answer:
Simplified = 5
Classification = Monomial
Step-by-step explanation:
<h2>PART I: Simplify the expression</h2><u>Given expression:</u>
3x² + 6x + 5 - 3x (2 + x)
<u>Expand parenthesis by distributive property:</u>
= 3x² + 6x + 5 - 3x (2) - 3x (x)
= 3x² +6x + 5 - 6x - 3x²
<u>Put like terms together:</u>
= 3x² - 3x² + 6x - 6x + 5
= 0 + 0 + 5
=
<u>Concept:</u>
Polynomial is classified by the number of terms a polynomial has.
- Monomial: a polynomial with only one term
- Binomial: a polynomial with two terms
- ...
<u>Classify the given expression:</u>
Original = 3x² + 6x + 5 - 3x (2 + x)
Simplified = 5
5 is a constant and it has only one term
Therefore, it is a <u>monomial</u>.
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Answer:
-2, 8/3
Step-by-step explanation:
You can consider the area to be that of a trapezoid with parallel bases f(a) and f(4), and width (4-a). The area of that trapezoid is ...
A = (1/2)(f(a) +f(4))(4 -a)
= (1/2)((3a -1) +(3·4 -1))(4 -a)
= (1/2)(3a +10)(4 -a)
We want this area to be 12, so we can substitute that value for A and solve for "a".
12 = (1/2)(3a +10)(4 -a)
24 = (3a +10)(4 -a) = -3a² +2a +40
3a² -2a -16 = 0 . . . . . . subtract the right side
(3a -8)(a +2) = 0 . . . . . factor
Values of "a" that make these factors zero are ...
a = 8/3, a = -2
The values of "a" that make the area under the curve equal to 12 are -2 and 8/3.
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<em>Alternate solution</em>
The attachment shows a solution using the numerical integration function of a graphing calculator. The area under the curve of function f(x) on the interval [a, 4] is the integral of f(x) on that interval. Perhaps confusingly, we have called that area f(a). As we have seen above, the area is a quadratic function of "a". I find it convenient to use a calculator's functions to solve problems like this where possible.
