Question

If f (x) = x^19 - 19x^18 + 18x^17 + x^5 - 19x^4 + 18x^3 - 17 the. f (18) is

a)0
b)17
c)-17
d)18

Answer 1

Given :

$\tt If\: f (x) = x^{19} - 19x^{18} + 18x^{17} + x^5 - 19x^4 + 18x^3 - 17 the\:f (18) is$

Solution :

$\tt \: f (x) = x^{19} - 19x^{18} +18x^{17} + {x}^{5} - {19x}^{4} + {18x}^{3} - 17 \\ \\ \tt = {x}^{17} ( {x}^{2} - 19x + 18) +( {x}^{17} + {x}^{3} ) - 17 \\ \\ \tt = ( {x}^{2} - 19x + 18)( {x}^{17} + {x}^{3}) - 17 \\ \\ \\ \tt \: f(18) = ( {(18)}^{2} - 19(18) + 18)({x}^{17} + {x}^{3}) - 17 \\ \\ \tt = (324 - 324 + 18)({x}^{17} + {x}^{3}) - 17 \\ \\ \tt = (0)({x}^{17} + {x}^{3}) - 17 \\ \\ \boxed {\boxed{ { \purple{ \bold{{= - 17}}}}}}$

Hence , the correct answer is -17 ( option (c) is the right answer)

Answer 2

Answer :-

Value of f( 18 ) = - 17 [ Option ' c ' ]

Given :-

Polynomial : f( x ) =  x¹⁹ - 19x¹⁸ + 18x¹⁷ + x⁵ - 19x⁴ + 18x³ - 17

To Find :-

Value of f( 18 )

Solution :-

❍ To calculate the answer of the question we must know that ::

Value of a polynomial -

•  The value of a polynomial p( x ) at x = a is obtained by substituting x = a in p( x ) and is denoted by p( a ).

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Finding the value :-

• By putting the value of x as 18 everywhere.

⤳ f( 18 ) = ( 18 )¹⁹ - ( 19 × 18 )¹⁸ + ( 18 × 18 )¹⁷ + ( 18 )⁵ - ( 19 × 18 )⁴ + ( 18 × 18 )³ - 17

⤳ f( 18 ) = 18¹⁹ - 18¹⁹ - 18¹⁸ + 18¹⁸ + 18⁵ - 18⁵ - 18⁴ + 18⁴ - 17

⤳ f( 18 ) = 0 - 17

⤳ f( 18 ) = -17

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Henceforth, the value of f( 18 ) is - 17.