Download exponents, and in which variables appear only in the numerator.

FPC 10 Polynomial Operations:
+
A polynomial is a term(monomial) or sum of terms, in which all variables have whole number
exponents, and in which variables appear only in the numerator .
A monomial is a number, or a variable, or the product of numbers and variables;
it is a polynomial with only one term
A binomial is a polynomial with two terms, a trinomial is a polynomial with three terms.
Example 1: Consider the following algebraic expressions. In each case:
State whether the expression represents a polynomial or not.
If the expression does not represent a polynomial, explain why.
Example 3: A triangle has a perimeter of (17m + 5n). One side measures (3m – 2n) and the other side
measures (5n + m). Write and simplify an expression for the length of the third side of the triangle.
Example 4: Fill in the blank.
a) The expression 3x2 is called a _________________________
b) In the term -4x3, the coefficient is ______________, and the exponent is ___________
c) The number of terms in the expression 3x3 – x2 + 2 is _____. The constant term is __________.
d) -x2y3z is a ________________ with a leading coefficient ____.
e) When 3x2 – 2x + 1 is evaluated for x = -3, the result is ____________.
f) 3x6 + 2x2 – 5 is a ___________________ with a leading coefficient ____.
Example 5: Simplify and write in descending order of powers. State the leading coefficient.
a) -2x3 – 2x2 – 2x3 + 2x2
b) 3y4 – 2y2 – y4 – 2y
Multiplying a Polynomial by a Monomial
Example 6: Find the area of each figure
a)
b)
4x2
8x
4x - 5
2x - 3
Example 7: Simplify each product
a) 2n(9n2 – 2n - 12)
b) 8x(3x +y) – y(2x – 3y)
c) 8x2(2x2 – 4x + 4)
d)  1 xy 2 ( 2 xyz  1 x  8)
2
3
3
e) u(7u - 2) + 25u
f) 5b(-b2 + 7b - 1) + 9(3b2- 6b + 2)
g) 4r2(3r - 7) + r(7r2 - 5r + 2) - 4(r2 + 9r)
h)
1
4
c(3c 3  3c  6)  (3c 2 6c)
3
3
i)
-2x(3x - 4) + 6x.
j)
8 – 2(5x + 11)
k) A rectangular garden is x feet wide. The length of the garden is 3 feet more than twice the width.
Write a polynomial that represents the area of the garden in square feet.