SOLUTION: Question: Use the synthetic division to find f(-4) if f(x) =x^4+20x^3+396+405. Possible Answers: (a) none of these (b) 6 (c) 7 (d) 5

Question 30352: Question:
Use the synthetic division to find f(-4) if f(x) =x^4+20x^3+396+405.
Possible Answers:
(a) none of these
(b) 6
(c) 7
(d) 5
Answer by sdmmadam@yahoo.com(530) (Show Source): You can put this solution on YOUR website!
Use the synthetic division to find f(-4) if f(x) =x^4+20x^3+396+405.
---- 1 20 138 396 405
(-4)| -4 -64 -296 -400
-------------------------------------
-----1 16 74 100 5

We observe that the remainder is 5 and therefore
Answer: f(-4) = 5
which is your choice (d) 5

Note: Leave out the x's and write down the numbers (called coefficients) of the first polynomial on the first line. Then put (-4) (which comes from [x-(-4)] on the second line.
Start by copying the first 1 onto the bottom line. Multiply by (-4) to get the (-4) and write in the second line underneath 20. Add the top 20 to this (-4) to get 16. Keep repeating this by multiplying each number on the bottom line by
(-4), and add the result to the top line, with the result of the addition going on the bottom line.
The last number is the remainder
Note: How is f(-4) = 5
the remainder got on division of f(x) by [x-(-4)] ?
Answer:: It is the Remainder theorm: If a polynomial f(x)
of degree n >1 is divided by the linear function (x-r),
the remainder is the number f(r)
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