In Exercises 17–32, divide using synthetic division. (3x^2+7x−20)...

Question

In Exercises 17–32, divide using synthetic division. (3x^2+7x−20)÷(x+5)

Accepted Answer

hey everyone here we are asked to use synthetic division to find the quotient of the quantity of seven X squared plus 16 X plus nine divided by the quantity of x minus one. So to do this using synthetic division we set up a div vision like format where on the right hand side we put each coefficient of X. So starting at the highest power of X squared has a coefficient of seven. Then moving on to X to the power of one, has a coefficient of 16. Then X to the zero power has a coefficient of nine. And now for the left hand side we need to take the opposite sign of the constant. Indeed divisor which in this case will be positive one. And so now to start solving, we begin by bringing down the first coefficient of seven without making any changes. We then bring it to the next column and multiply it by the constant of one which gives us seven times one which is equal to seven. We then add it to the other coefficient in the column, seven plus 16 gives us 23 And then we repeat doing 23 times one Which is just 23, 23 plus nine gives us 32 now we have all of our coefficients. And each of these coefficients aside from the last one is a coefficient of the quotient and matches up with the following X to whatever power except for the last coefficient which is the remainder. So it gets divided by the quantity of x minus one and therefore our solution, the quotient is seven X plus 23 plus 32 divided by the quantity of x minus one. And this is our answer here for choice. A 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. (3x^2+7x−20)÷(x+5)

Key Concepts

Synthetic Division

Polynomial Functions

Remainder Theorem