SOLUTION: which of the following polynomials has a factor of x-1?.
A) {{{p(x)=x^3+x^2-2x+1}}}
B) {{{q(x)=2x^3-x^2+x-1}}}
c) {{{r(x)=3x^3-x-2}}}
D) {{{s(x)=-3x^3+3x+1}}}
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-> SOLUTION: which of the following polynomials has a factor of x-1?.
A) {{{p(x)=x^3+x^2-2x+1}}}
B) {{{q(x)=2x^3-x^2+x-1}}}
c) {{{r(x)=3x^3-x-2}}}
D) {{{s(x)=-3x^3+3x+1}}}
Log On
In this case, x-k = x-1, so k = 1. Therefore, if we find a function p(x) such that p(k) = p(1) = 0 then we have found the answer.
Essentially we plug in x = 1 into each answer choice. Then we see which results in 0.
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Let's go through the answer choices one by one. Starting with choice A
Replace every x with 1
Since the result is NOT equal to 0, this means that x-1 is NOT a factor of p(x).
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Now onto choice B. Like before, plug in x = 1 to see if we get a result of 0.
Replace every 'x' with 1
Again we don't get 0. So choice B is not the answer either.
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Part C)
Plug in x = 1
We got a result of 0, so x-1 is a factor of r(x). We have our answer. Let's check part D just to complete the problem.
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Part D)
Plug in x = 1
The nonzero result means x-1 is not a factor of s(x)
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You can put this solution on YOUR website! .
which of the following polynomials has a factor of x-1?
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Those and only those that have the number "1" as their root.
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