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The cost of 6sandwiches and 4 drinks is $53. The cost of 4 sandwiches and 6 drinks is $47. How much does one sandwich cost?
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<u>Answer:</u>
If x-2 is a factor of p(x) = x^{4} - 3 x^{2} + 2 x - 8 ,then p(x) = 0
<u>Solution:</u>
According to factor theorem of polynomials,
x-a is a factor of polynomial p(x), if and only p(a)=0
<u>Step 1:</u>
Since x-2 is factor of p(x),
x - 2 = 0
x = 2
<u>Step 2:</u>
By substituting x = 2 in equation 1,
p(x) = 16 - 3(4 ) + 4 -8
p(x) = 16 - 12 - 4
p(x) = 16 - 16
p(x) = 0
Since x - 2 is a factor of p(x) , we get p(x)=0