Chapter B.4, Problem 1ED

Consider the points in Table 1.

(A)    Let $p_1\left(x\right)=a_0+a_1\left(x-1\right)$. Determine a₀ and a₁ so that the graph of y = p₁(x) passes through the first two points in Table 1.

(B)    Let $p_2\left(x\right)=a_0+a_1(x-1)+a_2(x-1)(x-2)$. Determine a₀, a₁, and a₂ so that the graph of y = p₂(x) passes through the first three points in Table 1.

(C)    Let

$p_3\left(x\right)=a_0+a_1\left(x-1\right)+a_2\left(x-1\right)\left(x-2\right)+a_3\left(x-1\right)\left(x-2\right)\left(x-3\right).$

Determine a₀, a₁, a₂, and a₃, so that the graph of y = p₃(x) passes through all four points in Table 1.

Table 1