Use Substitution to solve the system of equations. c+b=12 2b-3c=1 1/2
1 answer:
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Answer:
D
Step-by-step explanation:
If the polynomial p(x) is divided by a polynomial of the form x+k (which accounts for all of the possible answer choices in this question), the result can be written as
p(x)/x+k = q(x) + r/x+k
where q(x) is a polynomial and r is the remainder. Since x+k is a degree-1 polynomial (meaning it only includes and no higher exponents), the remainder is a real number.
Therefore, p(x) can be rewritten as p(x) = (x+k)q(x) + r, where r is a real number.
The question states that p(3) = −2, so it must be true that
−2 = p(3) = (3+k)q(3) + r
Now we can plug in all the possible answers. If the answer is A, B, or C, r will be 0, while if the answer is D, r will be −2.
A. −2=p(3)=(3+(−5))q(3)+0
−2=(3−5)q(3)
−2=(−2)q(3)
This could be true, but only if q(3)=1
B. −2=p(3)=(3+(−2))q(3)+0
−2=(3−2)q(3)
−2=(−1)q(3)
This could be true, but only if q(3)=2
C. −2=p(3)=(3+2)q(3)+0
−2=(5)q(3)
This could be true, but only if q(3) = −2/5
D. −2=p(3)=(3+(−3))q(3)+(−2)
−2=(3−3)q(3)+(−2)
−2=(0)q(3)+(−2)
This will always be true no matter what q(3) is.
Of the answer choices, the only one that must be true about p(x) is D, that the remainder when p(x) is divided by x−3 is -2.
The final answer is D.
The first step for solving this expression is to write the division as a fraction.
x +
× x
Calculate the product.
Remember that if a term doesn't have an exponent,, it is considered that the exponent for that term is 1. This changes the expression to the following:
Now multiply the terms with the same base by adding their exponents.
Finally,, add the numbers together to get your final answer.
x +
Let me know if you have any further questions.
:)
x +
Calculate the product.
Remember that if a term doesn't have an exponent,, it is considered that the exponent for that term is 1. This changes the expression to the following:
Now multiply the terms with the same base by adding their exponents.
Finally,, add the numbers together to get your final answer.
x +
Let me know if you have any further questions.
:)