Q&A for How to Divide Polynomials Using Synthetic Division

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How do I solve synthetic division if the divisor is more than three terms?

Community Answer

The divisor cannot be more than three terms. In synthetic division, the divisor is always in the form x-a.

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What is the benefit of synthetic division?

Community Answer

You can do it on a smaller piece of paper. Seriously, that's it. Synthetic is computationally identical to long division, but instead of writing powers of x everywhere, it uses its layout to keep the exponents straight.

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How do I solve a problem dividing a polynomial by 2x-1 in synthetic division?

Community Answer

2x-1 is actually the same as x-(1/2), so you can do synthetic division putting +(1/2) in the box.

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Where does the (x^2-4) come from?

Michael Carter

Community Answer

Under Step 11, after dividing you are left with 1 0 -4 and 16. The first 3 of these numbers are added to a new equation that is one less power than the original variables. Since we started with the equation x^3, we drop one power to x^2. This results in (1)x^2 + 0(x) + (-4), simplifying = x^2 - 4, which answers your question. But, we aren't done because we still have the remainder(R) of 16. To finish, see Step 12.

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Question

How do I divide a polynomial using synthetic division if the divisor is three or more than three terms?

Roger Doering

Community Answer

Here's an example of a 4th order divided by a second order: 16*x^4-5*x^3+x^2-2*x-7/2*x^2+x-6 8 -6.5 27.75 -2 -1 6 16 -5 1 -2 -7 -16 -8 48 0 -13 49 -2 -7 13 6.5 -39 0 55.5 -41 -7 -55.5 -27.75 166.5 0 -68.75 159.5 Answer: 8x^2 - 6.5x + 27.75 + (-68.75x + 159.5)/(2x^2 + x - 6)

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What if the divisor is 3x2+x+3, how do I solve it using synthetic division?

Community Answer

Synthetic division is not capable of handling quadratic divisors or above. Use long polynomial division instead.

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When the remainder is not equal to zero, then what do I do?

Community Answer

Synthetic division allows you to find both the quotient and the remainder of the division; the last number would be the remainder, while the previous numbers are the quotient, as seen above. If the last number, the remainder, is 0, the divisor is a factor of the dividend.

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Question

What is the formula for synthetic division?

Community Answer

It is not a formula, it's a method. Read the article for detailed instructions.

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Question

How do I divide this way if I have two divisors like (a^2-28) / (a-5)?

Community Answer

Supposing that your “/“ indicates a division inside of the division: You multiply by (a-5) and divide by (a^2-28).

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What is (r³ + 2r² -7r - 12) ÷ (r + 3)?

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The answer is r² - 2r - 1 with a remainder of zero.

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