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Find the remainder when f(x) = 4x3 − 20x − 50 is divided by x − 3.

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Naǫid
Use the remainder theorem: when you divide a polynomial f(x) by (x-a), the remainder is f(a).

[tex](4x^3-20x-50) \div (x-3) \\ \\ a=3 \\ \\ r=f(3)=4 \times 3^3-20 \times 3-50=4 \times 27-60-50=108-110=-2[/tex]

The remainder is -2.
Carlosegoid

For this case what we have to take into account in the polynomial division is the following:

1) In the product of two variables, if we have the same base, the exponents are added

2) We can only add or subtract coefficients from variables that have the same exponent.

3) The Remainder and the quotient are:

Quotient: 4x ^ 2 + 12x + 16

Remainder: -2

Answer:

The remainder is -2. See attached image for the solution.

View image Carlosego

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