Find the values of a & b so that x^4+x^3+ax+b is divisible by x^2+1

a = 1 b = -1.

Step-by-step explanation:

Suppose the quotient when you divide x^4+x^3+ax+b  by x^2 + 1 is

x^2 + ax + b then expanding we have:

(x^2 + 1)(x^2 + ax + b)

= x^4 + ax^3 + bx^2 + x^2 + ax + b

= x^4 + ax^3 + (b + 1)x^2 + ax + b Comparing this with the original expression:

  x^4 +  x^3  + 0 x^2       + ax + b  Comparing coefficients:

a = 1 and b+ 1 = 0 so b = -1.

answer: h

step-by-step explanation:

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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step-by-step explanation: