In Exercises 17–32, divide using synthetic division. (6x^5−2x^3+4...

Question

In Exercises 17–32, divide using synthetic division. (6x^5−2x^3+4x^2−3x+1)÷(x−2)

Accepted Answer

hey everyone here we are asked to use synthetic division to find the quotient of the quantity of seven X to the fifth power minus three. X to the third power plus X squared minus five X plus two. All divided by the quantity of x minus five. So to solve this we have to set up a division like format where on the right hand side will have all of the coefficients starting with the highest power of X. To the fifth power. It has a coefficient of seven and I will continue all the way till X to the zero power. So next is X to the power of four which has a coefficient of zero. Then we have X to the power of three which is negative three, X squared is one X to the first power is negative five and X to the zero power is to and next we have to find the number for the left hand side. And to do this we just take the opposite sign of the constant in the divisor. Or you can also set the divisor x minus five equal to zero, showing that X is five. So we'll put five on the left hand side. And next to start solving, we begin by bringing the first coefficient down which is seven without making any changes. We then bring it to the next column and multiply it by five. So we get seven times five which gives us 35 add it to the other coefficient in the column. 35 plus zero is just 35. And then we repeat this process. So we then take 35 times five, which gives us 175. 175 plus plus negative three is 172. Then we do 172 times five, which is equal to 868 plus one is 861. Then 861 times five gives us 4305 plus negative five gives us 4300. And finally 4300 times five gives us 21,500 plus two is 21,502. And so now we have all of our coefficients and each of these coefficients, aside from the last one are coefficients of the quotient. So they line up with each 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 -5. So in conclusion, our quotation is seven X to the fourth Power plus 35 X. To the third Power plus 172 X. To the second Power plus 861 X plus 4300 finally plus 21,502 divided by the quantity of X minus five. 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. (6x^5−2x^3+4x^2−3x+1)÷(x−2)

Key Concepts

Synthetic Division

Polynomial Coefficients

Remainder Theorem