Given the polynomial 21x^4+3y-6x^2+34 1. What polynomial must be subtracted from it to obtain 29x^2-7? 2. What polynomial must b
1 answer:
Answer:
must be subtracted
As you can see, we added -x+2 to this polynomial to obtain a first degree polynomial. (Though really anything with an x would do. For example, 3x, 2221x, or -224x would all work)
Step-by-step explanation:
We have the following polynomial
And need to find a polynomial to subtract from it to get
This means that if we subtract these two polynomials, we will get our desired polynomial
Just to be sure, we can then check our work by finding the difference of the first polynomial and the one that we just found
As we got the desired result, we know that this answer is correct.
And now for the second part of the problem. What polynomial must be added to it to obtain a first degree polynomial?
Recall that a first degree polynomial is one that has the total sum of 1. For example the polynomial x+5 is a first degree polynomial, but x+y+5 has a degree of 2.
This means that our desired polynomial needs to only have some amount of x's and constants.
We can do the same thing as the first time and simply subtract our desired result from the first polynomial. For simplicity, let us use the simple polynomial x+2
As you can see, we added -x+2 to this polynomial to obtain a first degree polynomial. (Though really anything with an x would do. For example, 3x, 2221x, or -224x would all work)
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Answer:
Bob will need of sod
Step-by-step explanation:
step 1
Find the area of the backyard
step 2
Find the area of the flower garden
step 3
Find the difference
We have the expression 
; to find the common denominator we are going to decompose each one of the denominators into prime factors, and then we are going to multiply the common factors raised to the highest power and all the non common factors.
The denominators of our fractions are 3, 6, and 9. 3 is already a prime, so we are going to let that one alone. 6 on the other hand is divisible by tow, so it can be decomposed into tow prime factors 2 and 3:
.
9 is divisible by 3, so it can also be decomposed into tow prime factors 3 and 3:
.
We have a common factor 3 in all our denominators, and among them the one raised to the highest power is
. On the other hand we only have one non-common factor, 2. So, our common denominator will be:
Now we know that the common denominator of our standard form fraction is 18, the only thing left is convert the denominators of each one of our fractions to 18 and simplify. To do that we are going to divide the common denominator by the denominator of each fraction, and then multiply the quotient by each one of the numerators:
Answer:
The denominators of our fractions are 3, 6, and 9. 3 is already a prime, so we are going to let that one alone. 6 on the other hand is divisible by tow, so it can be decomposed into tow prime factors 2 and 3:
9 is divisible by 3, so it can also be decomposed into tow prime factors 3 and 3:
We have a common factor 3 in all our denominators, and among them the one raised to the highest power is
Now we know that the common denominator of our standard form fraction is 18, the only thing left is convert the denominators of each one of our fractions to 18 and simplify. To do that we are going to divide the common denominator by the denominator of each fraction, and then multiply the quotient by each one of the numerators:
Answer: