Question

Divide.

>
(6x²+27x+17) = (x+4)
Your answer should give the quotient and the remainder.
Quotient:
Remainder:
X
Ś

Answer 1

• Quotient: 6x+3
• Remainder: 5

Explanation:

You want the quotient and remainder from division of (6x² +27x +17) by (x +4).

Synthetic division

Synthetic division of a polynomial by a monic binomial is an easy way to perform the division without a lot of writing. The attachment pretty well describes the process.

The result is a quotient of 6x +3, and a remainder of 5.

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Additional comment

A "monic" polynomial is one that has a leading coefficient of 1.

The number at upper left in the synthetic division tableau is the zero of the divisor. Using the negative of the divisor constant means we can add partial products, saving the confusion and error associated with subtraction.