<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
the new radius be to meet the client's need is 4.9 cm .
<u>Step-by-step explanation:</u>
Here we have , can company makes a cylindrical can that has a radius of 6 cm and a height of 10 cm. One of the company's clients needs a cylindrical can that has the same volume but is 15 cm tall. We need to find What must the new radius be to meet the client's need . Let's find out:
Let we have two cylinders of volume with parameters as follows :
We know that volume of cylinder is , According to question volume of both cylinder is equal i.e
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⇒
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⇒ Putting all values
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Therefore , the new radius be to meet the client's need is 4.9 cm .