Basic Mathematics for College Students

Appendix II Polynomials A-7

WHYTo evaluate a polynomialmeans to find its numerical value, once we know
the value of its variable.

Solution
a. Substitute 3 for x.

Multiply: 3(3) 9.

Subtract.

b. Substitute 3 for x.

Evaluate the exponential expression.

Multiply: 2(9) 18.

Add:  18  3 15.

  18 Subtract:  15  3  15 (3) 18.

  15  3

  18  3  3

  2192  3  3

 2 x^2 x 3  21322  3  3

 7

 9  2

3 x 2  3132  2

Self Check 3

Evaluate each polynomial for

x1:

a. 2 x^2  4

b. 3 x^2  4 x 1

Now TryProblems 23 and 31

EXAMPLE (^4) Height of an Object The polynomial  16 t^2  28 t 8
gives the height (in feet) of an object tseconds after it has been thrown into the air.
Find the height of the object after 1 second.
StrategyWe will substitute 1 for tand evaluate the polynomial.
WHYThe variable trepresents the time since the object was thrown into the air.
Solution
To find the height at 1 second, we evaluate the polynomial for t1.
Substitute 1 for t.
Evaluate the exponential expression.
Multiply: 16(1) 16 and 28(1) 28.
Add:  16  28 12.
Add.
At 1 second, the height of the object is 20 feet.

 20

 12  8

  16  28  8

  16112  28112  8

 16 t^2  28 t 8  161122  28112  8

Self Check 4

Refer to Example 4. Find the

height of the object after

2 seconds.

Now TryProblems 35 and 37

1. a.binomial b.monomial c.trinomial 2. a. 3 b. 8 c. 7


2. a. 6 b. 8 4.0 ft

ANSWERS TO SELF CHECKS

Fill in the blanks.

1. A polynomial with one term is called a.


2. A polynomial with three terms is called a.


3. A polynomial with two terms is called a.


4. The degree of a polynomial is the same as the degree
   of its term with degree.

VOCABULARY

Classify each polynomial as a monomial, a binomial, or a

trinomial.

5. 3 x^2  4 6. 5 t^2 t 1


6. 17 e^4 8. x^2 x 7


7. 25 u^2 10. x^2  9


8. q^5 q^2  1 12. 4 d^3  3 d^2

CONCEPTS

SECTION II.1 STUDY SET