The question is asking us to perform the synthetic division of the polynomial 2x^2 - 7x + 10 by x - 5.
Here are the steps to solve this:
Step1: Write the coefficients of the dividend polynomial which are 2, -7, and 10.
Step 2: Now write the zero of the divisor polynomial x - 5 which is 5.
Step 3: Draw a line, place the coefficients above it, and your zero to the left of it. Starting from left, bring down the first coefficient (2 in our case) and put it below the line.
Step 4: Now multiply this first value below the line by the zero (5), and write this result (10) under the second coefficient from the left (-7).
Step 5: Add these two values together, which is -7 + 10 to get 3. Write this below the line.
Step 6: Now multiply the value below the line (3) by the zero (5) to get 15, and write this result under the next coefficient from the left (10).
Step 7: Add these two values together, that is, 10 + 15 to get 25. Write this below the line.
Now look what we have under the line. These are the coefficients of the quotient polynomial and the remainder. The coefficient 2 is the constant term of the quotient, the second one (3) is the coefficient of x in the quotient, and the last one (25) is the remainder.
So, we have a quotient of 2x + 3 and a remainder of 25 after the synthetic division of 2x^2 - 7x + 10 by x - 5.
Keep in mind that all the steps above correspond to the synthetic division method which is a quick way to perform the division of polynomials.