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.
+9466 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
+9466 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
