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.

Guest Jun 28, 2019

#1**+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

hectictar Jun 28, 2019

#2**+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 x^{2} in them, we would get 0

(-4x^{2})(-7) + (2x)(tx) + (-5)(x^{2}) = 0

28x^{2} + 2tx^{2} - 5x^{2} = 0

Factor x^{2} out of all the terms on the left side.

x^{2}( 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

hectictar Jun 28, 2019