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- Good morning class. Yesterday, we discussed the long division. Today, we're going to talk about how to use the Synthetic Divsion.
- SYNTHETICDIVISION
- Synthetic division is a shortcut that can be used when the divisor is a binomial in the form x – k. In synthetic division, only the coefficients are used in the division process.
- As we all know the divisor is x-2. We will bring down the opposite sign of the coefficient which is positive 2 = k.
- For instance, let's divide x² - 14x + 24 by x-2.
- Next, we will write the coefficients of the dividend separated by spaces. Then bring down the leading coefficient which is 1.
- We will now multiply the leading coefficient by 2. Then, write the product in the next column which is also 2.
- Solution:x² - 14x + 24 / x-2 2 1 -14 24 2 1
- Solution:x² - 14x + 24 / x-2 2 1 -14 24 2 -24 1 -12 0
- After that, we'll add the terms of the second column and that will be -12.
- Afterwards, we will add the terms of the last column resulting to 0.
- Next, multiply the result which is -12 by 2. Then, write the product, -24, on the last column.
- Solution:x² - 14x + 24 / x-2 2 1 -14 24 2 -24 1 -12 0Quotient: x - 12
- Remember that the number in the last column is the remainder and has a degree of 0.
- We will use now the bottom numbers to write the quotient.
- 1 will be x then copy -12.
- Goodbye, sir Buenavista!
- Therefore, the final answer or result is x - 12 . The remainder is 0. So x - 12 is a factor of the original polynomial.
- Solution:x² - 14x + 24 / x-2 2 1 -14 24 2 -24 1 -12 0
- That ends our discussion for today. See you tomorrow, class.
- Quotient:: x - 12Final Answer: x² - 14x + 24 / x-2 = x - 12
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