Chapter Dividing polynomials

Objectives  Use long division and synthetic division to divide polynomials.

Dividing Polynomials  Polynomial long division is a method for dividing a polynomial by another polynomials of a lower degree. It is very similar to dividing numbers.

Example#1  Divide using long division.  (– y y ) ÷ ( y – 3)

Example#2  Divide using long division  (15 x x – 12) ÷ (3 x + 1)

Student guided practice Do problems 1-6 in the worksheet

Synthetic division  Synthetic division is a shorthand method of dividing a polynomial by a linear binomial by using only the coefficients. For synthetic division to work, the polynomial must be written in standard form, using 0 and a coefficient for any missing terms, and the divisor must be in the form (x – a).

Example#3  Divide using synthetic division.  (3 x x – 2) ÷ ( x –1/3 )

Example#4  Divide using synthetic division.  (3 x 4 – x x – 1) ÷ ( x + 2)

Student guided practice  Do problems 5-7 in your book page 170

Dividing Polynomials  You can use synthetic division to evaluate polynomials. This process is called synthetic substitution. The process of synthetic substitution is exactly the same as the process of synthetic division, but the final answer is interpreted differently, as described by the Remainder Theorem.

Dividing Polynomials

Example#5  Use synthetic substitution to evaluate the polynomial for the given value.  P ( x ) = 2 x x 2 – x + 7 for x = 2.

Example#6  Use synthetic substitution to evaluate the polynomial for the given value.  P ( x ) = 6 x 4 – 25 x 3 – 3 x + 5 for x = – 1/3.

Geometry Application  Write an expression that represents the area of the top face of a rectangular prism when the height is x + 2 and the volume of the prism is x 3 – x 2 – 6 x.

Algebra Application  Write an expression for the length of a rectangle with width y – 9 and area y 2 – 14 y + 45.

Student guided practice  Do problems 5-10 in your book page 170

Homework  Do problems 16-18,20-23,25-27 in your book page 170

Closure  Today we learned about dividing polynomials.  Next class we are going to learned how to factor polynomials.