In the table shown, the formula relating $x$ and $y$ is:
$x$ $1$ $2$ $3$ $4$ $5$
$y$ $3$ $7$ $13$ $21$ $31$

y = 4 x - 1

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y = x^{3} - x^{2} + x + 2

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y = x^{2} + x + 1

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y = (x^{2} + x + 1) (x - 1)

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None of these

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Solution

The correct option is D $y = x^{2} + x + 1$
(C) is shown to be the correct choice by direct check.
Note: The fact the y-differences are $4, 6, 8$ and $10$ can be used to eliminate $(a)$ and $(b)$ immediately.

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In the table shown, the formula relating x and y is:x12345y37132131

The correct option is D y=x2+x+1(C) is shown to be the correct choice by direct check.Note: The fact the y-differences are 4,6,8 and 10 can be used to eliminate (a) and (b) immediately.

In the table shown, the formula relating $x$ and $y$ is:
$x$ $1$ $2$ $3$ $4$ $5$
$y$ $3$ $7$ $13$ $21$ $31$

The correct option is D $y = x^{2} + x + 1$
(C) is shown to be the correct choice by direct check.
Note: The fact the y-differences are $4, 6, 8$ and $10$ can be used to eliminate $(a)$ and $(b)$ immediately.