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WAEC Further Mathematics 2012 Paper

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Question : 9

Total: 40

A polynomial is defined by

f(x + 1) = x^{3} + px^{2} - 4x + 2

, find f(2).

-8
-2
2
8

Solution:

Concept:

To find

f(2)

from

f(x+1)

, set the input equal to

2

and solve for

x

.

Explanation:

The polynomial is given as

f(x+1)=x^{3}+3x^{2}-4x+2

.

To evaluate

f(2)

, make the argument equal to

2

.

So

x+1=2

, which gives

x=1

.

Substitute

x=1

into the polynomial:

f(2)=1^{3}+3(1)^{2}-4(1)+2

=1+3-4+2

=2

.

Answer:

f(2)=2

, so the correct option is C.

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