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The synthetic division calculator will calculate the quotient and remainder of the given divisor and dividend. The synthetic division solver makes it possible to find the answer only by using the coefficient of the polynomials.
The division of polynomials is a special case of dividing a polynomial expression by a linear factor. It is used for determining the zeros of the polynomial by the division method. In the synthetic division method, the leading coefficient should equal 1. The synthetic division is normally used to find the zero of the polynomial with a zeros calculator
The formula of synthetic division is stated as follows.
Where
P(x) = Dividend Polynomial of Any Order
(x-c) = Linear Factor of Degree “1”
Q(x) = Quotient
R = Remainder
You can do synthetic division manually but it’s a challenging task, The following steps are used by the divide using a polynomial synthetic division calculator with steps for the division process:
Write down the quotient and the remainder of the synthetic division
Let’s conduct the synthetic division with the dividend as 7x^3 + 4x + 8 and the divisor x + 2.
Given:
Dividend = 7x^3 + 4x + 8
Divsor = x + 2
\(frac {7x^3 + 4x + 8}{x + 2}\)
Coefficient of the numerator and denominator polynomial of first-degree binomial expression are:
$$ 7, 4, 8 $$
$$ X + 2 = 0 $$
$$ X = −2.0 $$
The problem with the division format
$$\begin{array}{c|rrrrr}&x^{3}&x^{2}&x^{1}&x^{0}\\-2.0&7&0&4&8\\&&\\\hline&\end{array}$$
Carry down the leading coefficient to the bottom row
\( \begin{array}{c|rrrrr}-2.0&7&0&4&8\\&&\\\hline&7\end{array} \)
$$ 7∗(−2.0) = −14 $$
\( \begin{array}{c|rrrrr}-2.0&7&0&4&8\\&&-14&\\\hline&7&\end{array} \)
$$ 0 + (−14) = −14 $$
\( \begin{array}{c|rrrrr}-2.0&7&0&4&8\\&&-14&\\\hline&7&-14&\end{array} \)
Multiply the obtained value by the zero of the denominators, and put the outcome into the next column
$$ −14 ∗ (−2.0) = 28 $$
\( \begin{array}{c|rrrrr}-2.0&7&0&4&8\\&&-14&28&\\\hline&7&-14&\end{array} \)
Add down the column
$$ 4 + (28) = 32 $$
\( \begin{array}{c|rrrrr}-2.0&7&0&4&8\\&&-14&28&\\\hline&7&-14&32&\end{array} \)
The division solver multiplies the obtained value by the zero of the denominators and puts the outcome into the next column
$$ 32 ∗ (−2.0 ) = −64 $$
\( \begin{array}{c|rrrrr}-2.0&7&0&4&8\\&&-14&28&-64&\\\hline&7&-14&32&\end{array} \)
$$ 8 + (−64) = −56 $$
\( \begin{array}{c|rrrrr}-2.0&7&0&4&8\\&&-14&28&-64&\\\hline&7&-14&32&-56&\end{array} \)
So, the quotient is \( 7x^2−14x+32 \), and the division remainder is −56 Therefore, the Answer is:
$$ \frac{7x^3 + 4x + 8} {x + 2} $$
$$ 7x^2 − 14x + 32 − \frac {56} {x + 2} $$
Once entering the polynomial of the degree one in the synthetic division solver, then able to gather the result of the division by the coefficient of the variable.
The calculator functions to perform synthetic division of polynomial coefficients that you need to enter in it.
Let’s find out more about working!
Input:
Output:
From the source of Wikipedia: Regular synthetic division
From the source of Lumen Learning: Two Polynomials, Use Synthetic Division to Divide