Using Synthetic Division Divide −x3 + 4x2 + 9 by x − 3.

estT possible roots using synthetic division.

Synthetic division is a shorthand method of dividing polynomials for the special case of dividing by a linear factor whose leading coefficient is 1. .

Write polynomial division in the same format you use when dividing numbers.

.

. (x3 + 7x2 + 10x − 6) ÷ (x2 + 4x − 2) SOLUTION a. † Factor Theorem: c is a zero of P(x) if and only if x¡c is a factor of P(x).

estT possible roots using synthetic division.

2 3 Through synthetic division, we can do a sequence of operations that is much faster than traditional long division with polynomials. Then (– 2) is the remainder, –. .

. Determine if (x + 3) is a factor of (x) = 2x3 + x2 – 8x + 21 by using synthetic division.

3 Dividing Polynomials 175 Synthetic Division There is a shortcut for dividing polynomials by binomials of the form x − k.

There are 6 questions on either side.

However, synthetic division cannot be used to divide larger polynomials, like quadratics, into another polynomial. This method is shown in the next example.

Using Synthetic Division EXAMPLE 5 Use synthetic division to divide + 6x + S by x + 2. † Factor Theorem: c is a zero of P(x) if and only if x¡c is a factor of P(x).

(2x4 + 3x3 + 5x − 1) ÷ (x2 + 3x + 2) b.
You can use synthetic division whenever you need to divide a polynomial function by a binomial of the form x - c.
2.

.

.

One is the actual quotient and remainder you get when you divide the polynomial function by x - c. g. This shortcut is called synthetic division.

These methods are useful when both polynomials contain more than one term, such as the following two-term polynomial: 𝑥𝑥2 + 3. Polynomial Division Methods- Synthetic and Long Division This instructional aid was prepared by the Tallahassee Community College Learning Commons. Write polynomial division in the same format you use when dividing numbers. In algebra, synthetic division is a method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than long division. . MATH 10 LESSON PLAN.

To review Polynomial Long Division, watch the following set of YouTube videos introducing a review of long division, division by a monomial, long division of a polynomial by another polynomial, and synthetic division.

. In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that all this becomes second nature.

.

(2x4 + 3x3 + 5x − 1) ÷ (x2 + 3x + 2) b.

3 6 -19 1 6 18 -3 -6 6 -1 -2 0 (another root since no remainder).

If the polynomial P(x) is divided by x – c, then the remainder is the value P(c).

3 Dividing Polynomials 175 Synthetic Division There is a shortcut for dividing polynomials by binomials of the form x − k.