Question

How do you use synthetic division to evaluate `f(3)` given that `f(x)=x^3+2x^2-7x+8`?

Answer 1

To solve this using synthetic division, you need to start by drawing out some columns and a row, and filling in the coefficients for each leading power, in addition to your divisor (in this case 3; will go in the left most column). Consider the following diagram:

Now once you have that set up, bring your first coeff down. Then multiply it by the divisor. As shown:

Once you've done that, all you need to do is add the upper column number to what you have. Then, you simply multiply that by the divisor and move it over to the next column. Then repeat the process until you've reached the final column.

Now if you noticed, this is the exact same answer you'd get if you had directly plugged 3 into the function. Hence, just keep in mind that whenever you do synthetic division, you can always check your answer by plugging the divisor back into the function.

Hope that helped :)

Answer 2

To solve this using synthetic division, you need to start by drawing out some columns and a row, and filling in the coefficients for each leading power, in addition to your divisor (in this case 3; will go in the left most column). Consider the following diagram:

Now once you have that set up, bring your first coeff down. Then multiply it by the divisor. As shown:

Once you've done that, all you need to do is add the upper column number to what you have. Then, you simply multiply that by the divisor and move it over to the next column. Then repeat the process until you've reached the final column.

Now if you noticed, this is the exact same answer you'd get if you had directly plugged 3 into the function. Hence, just keep in mind that whenever you do synthetic division, you can always check your answer by plugging the divisor back into the function.

Hope that helped :)