Use synthetic division to divide the polynomial 2x3 – 45x + 28 by x + 5, and write the quotient polynomial and the remainder. [Be careful – notice that there is no x2 term.]. Show work.

I suggest you look up <synthetic division polynomial> with Google or use your course materials and give it a shot yourself. Then maybe you will stop thinking of yourself as a "math loser".

The answer I get is
2x^2 -10x +5 + 3/(x+5)

To divide the polynomial 2x³ - 45x + 28 by x + 5 using synthetic division, follow these steps:

Step 1: Arrange the coefficients of the dividend polynomial in descending order.

The dividend polynomial is 2x³ - 45x + 28. Arrange the coefficients in descending order: 2, 0, -45, 28.

Step 2: Set up the synthetic division tableau.

Since x + 5 has a coefficient of 1 for the x term, we set up a synthetic division tableau as follows:

-5 | 2 0 -45 28

Step 3: Perform the synthetic division.

Write the first coefficient, 2, below the horizontal line.

-5 | 2

Multiply -5 by 2 and write the result, -10, below the next coefficient (0).

-5 | 2
-10

Add the values in the second column, 2 + (-10) = -8, and write the result below the next coefficient (-45).

-5 | 2 -8
-10

Multiply -5 by -8 and write the result, 40, below the next coefficient (28).

-5 | 2 -8 40
-10

Add the values in the second column, -8 + 40 = 32, and write the result below the next coefficient (0).

-5 | 2 -8 40
-10 32

Step 4: Interpret the results.

The numbers in the last row represent the quotient and remainder. The result is read from left to right as follows:

Quotient: 2 - 8x + 40x²
Remainder: 32

Therefore, the quotient polynomial is 2 - 8x + 40x² and the remainder is 32.

The final division expression is: 2x³ - 45x + 28 = (x + 5)(2 - 8x + 40x²) + 32