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Suppose f is a polynomial such that f(0)=47, f(1)=32, f(2)=-13, and f(3)=16. What is the sum of the coefficients of f?

 

Find t if the expansion of the product of x^3 - 4x^2 + 2x - 5 and x^2 + tx - 7 has no x^2 term.

 Jun 28, 2019
 #1
avatar+8803 
+5

Suppose f is a polynomial such that f(0)=47, f(1)=32, f(2)=-13, and f(3)=16. What is the sum of the coefficients of f?

 

Depending on your definition of "coefficient", the answer is either

 

f(1)  =  32

 

which does count the constant term

 

or

 

f(1) - f(0)  =  32 - 47  =  -15

 

which does not count the constant term

 Jun 28, 2019
 #2
avatar+8803 
+5

Find t if the expansion of the product of x^3 - 4x^2 + 2x - 5 and x^2 + tx - 7 has no x^2 term.

 

If we add up all the tems that will have  x2  in them, we would get  0

 

(-4x2)(-7) + (2x)(tx) + (-5)(x2)  =  0

 

28x2 + 2tx2 - 5x2  =  0

                                       Factor  x2  out of all the terms on the left side.

x2( 28 + 2t - 5 )  =  0

                                       We only want to know what  t  will make this equal  0

28 + 2t - 5  =  0

 

23 + 2t  =  0

 

2t  =  -23

 

t  =  -11.5

 Jun 28, 2019

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