powerpoint presentattion

1. Subtitle

2. Polynomial is usually written in standard form in such a way
that the values of the exponents are in ascending order. The
degree of the term is the sum of the exponents of the variables of
a term. The degree of the polynomial is the term with the highest
exponent. The coefficient of the first term or the term with the
highest degree is called the leading term.

3. Polynomials According to
terms
According to
the degree
Degree(n)
1. 2x monomial linear 1
2. 3x2 - 1 binomial quadratic 2
3. x3 + 2x - 2 trinomial cubic 3
4. 2x4 + x2 – 4x + 1 polynomial quartic 4
5. x5 – 2x4 – x3 + 3x + 2 polynomial quintic 5
6. 2x6 – 5x3 - x trinomial 6th degree
polynomial
6
7. x7 + 3x
2
binomial 7th degree
polynomial
7

4. Polynomials Degree(n) Leading term
1. 2x + 5 1 2x
2. 3x2 + 3 2 3x2
3. x3 – 2x2 + x 3 x3
4. xy – 3x +25 2 xy
5. x3 + x2yz - 1 4 x2yz

5. The Factor Theorem
▪ The Factor Theorem: Given a real number c and a
polynomial function f(x), if f(c) = 0 then (x – c) is a factor of
f(x).
▪ The Converse of the Factor Theorem: Given a real
number c and a polynomial function f(x), if (x – c) is a
factor of f(x), then f(x) = 0.

6. Example 1.
Verify that (x + 4) is a factor of f(x) = x3 + 2x2 – 11x – 12.
Solution:
Equate (x + 4) to 0 then solve for x.
x +4 = 0
x = -4
Evaluate f(x) = x3 + 2x2 – 11x – 12
when x = -4
f(x) = x3 + 2x2 – 11x – 12
f(-4) = -43 + 2(-4)2 – 11(-4) – 12
f(-4) = -64 + 2(16) + 44 – 12
f(-4) = -64 + 32 + 44 – 12
f(-4) = -32 + 44 – 12
f(-4) = 12 - 12
f(-4) = 0
Since f(-4) =0 , by the Remainder Theorem, (x + 4) is a factor of f(x) = x3 + 2x2 – 11x – 12.

7. Example 2.
Show that (x – 3) is NOT a factor of f(x) = -2x3 + x2 – 5x + 22.
Solution:
Equate (x - 3) to 0 then solve for x.
x – 3 = 0
x = 3
Evaluate f(x) = -2x3 + x2 – 5x + 22
when x = 3.
f(x) = -2x3 + x2 – 5x + 22 when x = 3.
f(x) = -2(3)3 + (3)2 – 5(3) + 22
F(x = -2(27) + 9 – 15 + 22
F(3) = -54 + 9 – 15 + 22
F(3) = -45 – 15 + 22
F(3) = -60 + 22
f(x) = -38
Since f(x) = -38, (x – 3) is not a factor.

8. Polynomial or Not a Polynomial
1.2x - 3y (polynomial)
2.ab – c (polynomial)
3.2x + 4 (polynomial)
5
4. 6x – 2x3 + 21/2 (not)
5. x 3 - 1 (polynomial)
6. 2𝑥 - x3 + 1 (not)
7. x – 4 (polynomial)
2y
8. x-2 + 2x (not)
9. 9 . 2x (polynomial)
10. 2x3 – 5 (polynomial)
5

9. Complete the table by writing the degree, leading term and the
constant term.
Polynomial Degree Leading Term Constant Term
1. x2y – 5x
3 x2y 0
2. (x +3)(x + 2) = 1
2 x2 5
3. x3(x + 4) = -3
4 x4 3
4. 2x2 + 5 = 2x2 + 6
0 0 -1
5. 3x(x + 3)2
3 3x3 0