5.3 LONG DIVISION
REMEMBERING 4TH GRADE!!
Divide using long division
14 2615
Learning goal:
know and apply the Remainder Theorem: For a polynomial p(x) and a
number a, the remainder on division by x – a is p(a), so p(a) = 0 if
and only if (x – a) is a factor of p(x).
Dividing by a Polynomial
Ex 1 Simplify
x − 5 x 2 + 2 x − 30
Ex 2 Simplify
2
( x − 10 x − 24) ÷ ( x + 2)
Ex 3 Simplify
x 2 + x + 1 x3 + 3x 2 + 3x + 2
Ex 4 Is 2x+1 a factor of the polynomial?
2 x + 1 8x4 − 4 x2 + x + 4
Dividing by a Monomial
Ex 5 Simplify
24 x 3 y 2 − 16 xy 3 + 27 x 4 y
4x2 y2
5.3
Synthetic Division
Learning Goal
know and apply the Remainder Theorem: For a polynomial p(x) and a
number a, the remainder on division by x – a is p(a), so p(a) = 0 if and
only if (x – a) is a factor of p(x).
Synthetic division is a process
which allows you to divide a
polynomial by a BINOMIAL.
The binomial MUST BE
WRITTEN in the form
“x – r”
Synthetic Division Steps
1.
2.
3.
4.
5.
6.
Determine the value of r
Arrange polynomial in descending order
of degree
Place “0” terms in missing terms
locations
Write the coefficients in order
Use multiplication and addition to
manipulate the coefficients of the
quotient
Write the quotient using the coefficients
and beginning with a degree less than
the dividend
Use synthetic division to find the quotient
( x 3 − 4 x 2 + 6 x − 4) ÷ ( x − 2)
Use synthetic division to find the quotient
4
3
2
(b − 2b − 2b − 3b + 2) ÷ (b − 2)
Use synthetic division to find the quotient
(2 x3 + 4 x − 6) ÷ ( x + 3)
Use synthetic division to find the quotient
(4 y 4 − 5 y 2 + 2 y + 4) ÷ (2 y − 1)