Amber, bernie, and carlos are working on a problem together. their goal is to correctly apply the difference of cubes formula to factor 2x5−250x2.
here is their plan:
first, factor the greatest common factor out of the expression.
next, identify a and b.
finally, use the difference of cubes method to factor the expression.
each person followed the steps and arrived at a different answer. read each student’s work and identify who followed the steps correctly.
first, factor out 2x2: 2x5−250x2=2x2(x3−125). next, identify a and b: a=x, b=125. finally, follow the pattern to get 2x2(x−125)(x2+125x+15,625).
first, factor out x2: 2x5−250x2=x2(2x3−250). next, identify a and b: a=2x; b=250. finally, follow the pattern to get x2(2x−250)(4x2+500x−62,500).
first, factor out 2x2: 2x5−250x2=2x2(x3−125). next, identify a and b: a=x; b=5. finally, follow the pattern to get 2x2(x−5)(x2+5x+25).
which statements accurately analyze why each student is correct or incorrect?
there may be more than one correct answer. select all correct answers.
amber is incorrect because 125 is equal to b3, not b.
bernie is incorrect because x2 is not the gcf of the polynomial.
bernie is correct because he correctly factored the gcf, identified a and b, and applied the difference of cubes method.
carlos is incorrect because 5 is equal to b√3, not b.
carlos is correct because he correctly factored the gcf, identified a and b, and applied the difference of cubes method.
amber is correct because she correctly factored the gcf, identified a and b, and applied the difference of cubes method.
Carlos is correct
The first step is to factorize out 2x^2
This can be rewritten as
Recall, difference if cube (a^3-b^3)
= (a-b)(a^2 +ab + b^2)
from our equation,
b = 5.
So the difference of cubes will be
2x^2[(x-5) (x^2 + 5x + 5^2)]
=2x^2[(x-5) (x^2 + 5x + 25)]
Carlos followed these steps. So he is correct. Carlos is correct because he correctly factored the GCF, identified a and b, and applied the difference of cubes method.
Amber is incorrect because 125 is equal to b3, not b.
Bernie is incorrect because x2 is not the GCF of the polynomial. The GCF is 2x^2.
2 is A
3 is C
Hope this helps.
x/5+2 (I'm not sure about this one but the other two are polynomials)
2. a,b & c ?
A ) 7 x^7 - x - 5
C ) 4 x + √ x - 1
D ) x/5 + 2
2. Polynomials are:
A ) x² - x √2
C ) 2 + s
D ) 4 x³ + y
3. The polynomial: - 5 x³ - 4 x + 1 is:
C ) Cubic trinomial.
4. The degree of the polynomial: - 2 x² y^4 - 1/2 z is:
C ) 4
Explanation: The fields of mathematics, probability, and statistics use formal definitions of randomness. In statistics, a random variable is an assignment of a numerical value to each possible outcome of an event space. This association facilitates the identification and the calculation of probabilities of the events. Random variables can appear in random sequences. A random process is a sequence of random variables whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions. These and other constructs are extremely useful in probability theory and the various applications of randomness.
Randomness is most often used in statistics to signify well-defined statistical properties. Monte Carlo methods, which rely on random input (such as from random number generators or pseudorandom number generators), are important techniques in science, as, for instance, in computational science. By analogy, quasi-Monte Carlo methods use quasirandom number generators.
Question 1 :B,D.
Question 2:option B,
Question 4:option D.
Question 5: option c.
1) A polynomial can not have any exponent as a variable or a fraction.
Options B and D are polynomials.
2) The polynomial is having 3 terms and is of degree 3.so it is a cubic trinomial Option B.
3) Degree is the highest power of the variables in the terms .The term has the power=3+2=5
So degree =5.
Simplifying like terms,
35x^2 is a polynomial because it is a whole # and x is the product of the term, it also has a variable.
the other answer is x/5+2
The polynomial (x+4)(x-1)(x-2)(x-4) has zeros at x=-4,1,2,4.
The related polynomial equation is (x+4)(x-1)(x-2)(x-4)=0.
In order for this equation to be true at least one of the factors must by 0 that is the only way a product can be zero (if one of it's factors is).
So you wind up needing to solve these 4 equations:
x+4=0 x-1=0 x-2=0 x-4=0
x=-4 x=1 x=2 x=4
First equation, I subtracted 4 on both sides.
Second equation, I added 1 on both sides.
Third equation, I added 2 on both sides.
Fourth equation, I added 4 on both sides.
-4,1,2,4 are all integers
Integers are real numbers.
If all the power of the variables are greater than or equal to zero, then the expression is a valid polynomial.
2 + s
are all polynomials.
If the degree of the polynomial is 3, then it is a cubic polynomial. If the number of terms of a polynomial is 3, then it is a trinomial.
Hence, is a cubic trinomial.
The highest power is the degree.
Hence, degree of the polynomial is 2 + 4 = 6.
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just copy and paste it.
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