If f, left bracket, x, right bracket, equals, 2, x, to the power 5 , plus, 5, x, minus, 1f(x)=2x 5 +5x−1, then what is the remainder when f, left bracket, x, right bracketf(x) is divided by x, plus, 3x+3?

The question seems to be a bit mixed up, but I believe you're asking for the remainder when the polynomial function f(x) = 2x^5 + 5x - 1 is divided by x + 3.

Here's how you can find the remainder:

1. Set up the polynomial division: (2x^5 + 5x - 1) ÷ (x + 3).
2. Use synthetic division or long division for polynomials. In this case, synthetic division is simpler.

Here's how you do synthetic division:

• Write down the coefficients of the dividend (the polynomial to be divided), which are 2 (from 2x^5), 0 (there's no x^4 term), 0 (there's no x^3 term), 0 (there's no x^2 term), 5 (from 5x), and -1 (the constant term).
• Write down the zero of the divisor (the polynomial you're dividing by). The zero is the solution to the equation x + 3 = 0, which is x = -3.
• Now perform the synthetic division. Bring down the first coefficient (2), multiply it by the zero (-3), write the result under the next coefficient (0), add them together, and repeat this process for all coefficients.

The synthetic division should look like this:

    _______________________

-3 | 2 0 0 0 5 -1 | -6 18 -54 162 -507 ------------------------- 2 -6 18 -54 167 -508

3. The last number you get (-508) is the remainder when f(x) = 2x^5 + 5x - 1 is divided by x + 3. So, the remainder is -508.