In Exercises 17–32, divide using synthetic division. (4x^3−3x^2+3...

Question

In Exercises 17–32, divide using synthetic division. (4x^3−3x^2+3x−1)÷(x−1)

Accepted Answer

hey everyone here we are asked to use synthetic division to determine the quotient of the quantity of five X cubed minus two, X squared plus two, X minus four, divided by the quantity of x minus two. So to solve this, we have to set up a division like format where on the right hand side we have all of the coefficients of X. So starting at the highest power of X cubed, we have a coefficient of five. Then moving to X squared, we have negative two, X to the first power, we have positive two and X to the zero power, we have negative four. And then for the left hand side we have to take the opposite sign of the constant in the divisor which in this case is positive two. So next to start solving we begin by bringing down the first coefficient which is fine without making any changes. We then bring it to the next column and multiply it by this constant of two. So we have five times two which is equal to 10. And then we added to the other coefficient in that column. So 10 plus negative two gives us eight and then we repeat this process. So we'll have eight times two which gives us 16 plus two gives us 18 and then 18 times two gives us 36 plus negative four gives us 32. So now each of these coefficients, aside from the last one are coefficients of the quotient. So they each match up with the following x power. So this is all aside from the last coefficient which is the remainder, so it gets divided by the quantity of X -2. So therefore our solution, the quotient is five X squared plus eight x plus 18 plus 32 divided by the quantity of x minus two. And this is our answer here for choice D. Thanks for watching. I hope you found this video helpful, and I'll see you again next time.

In Exercises 17–32, divide using synthetic division. (4x^3−3x^2+3x−1)÷(x−1)

Key Concepts

Synthetic Division

Polynomial Functions

Remainder Theorem