How do you use synthetic substitution to find #f(x)# for x=2 given #f(x)=7x^4-3x^3+x^2+5x-9#?

Answer 1

#f(2) = 93#

#{: (,"|",7,-3,+1,+5,-9), (+,"|",,14,22,46,102), (,,"-----","-----","-----","-----","-----"), (xx(2),"|",7,11,23,51,color(red)(93)) :}#

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Answer 2

Sadie Ackerman

To use synthetic substitution to find ( f(x) ) for ( x = 2 ) given ( f(x) = 7x^4 - 3x^3 + x^2 + 5x - 9 ), follow these steps:

Write down the coefficients of the polynomial ( f(x) = 7x^4 - 3x^3 + x^2 + 5x - 9 ).
Start by bringing down the coefficient of the highest degree term, which is 7 in this case.
Multiply the number you brought down by the given value of ( x ), which is 2 in this case.
Add the result to the next coefficient (in this case, -3).
Repeat steps 3 and 4 until you reach the constant term.

By following these steps, you will find the value of ( f(x) ) when ( x = 2 ) using synthetic substitution.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.