Warm-Up Exercises Rewrite a polynomial EXAMPLE 1 Write 15x – x 3 + 3 so that the exponents...
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Transcript of Warm-Up Exercises Rewrite a polynomial EXAMPLE 1 Write 15x – x 3 + 3 so that the exponents...
Warm-Up ExercisesRewrite a polynomialEXAMPLE 1
Write 15x – x3 + 3 so that the exponents decrease from left to right. Identify the degree and leading coefficient of the polynomial.
SOLUTION
Consider the degree of each of the polynomial’s terms.
The polynomial can be written as – x3 +15 + 3. The greatest degree is 3, so the degree of the polynomial is 3, and the leading coefficient is –1.
15x – x3 + 3
Warm-Up Exercises
Tell whether is a polynomial. If it is a polynomial, find its degree and classify it by the number of its terms. Otherwise, tell why it is not a polynomial.
EXAMPLE 2 Identify and classify polynomials
5th degree binomialYes7bc3 + 4b4c
No; variable exponentn– 2 – 3
No; variable exponent6n4 – 8n
2nd degree trinomialYes2x2 + x – 5
0 degree monomialYes9
Classify by degree and number of terms
Is it a polynomial?Expression
a.
b.c.d.e.
Warm-Up ExercisesEXAMPLE 3 Add polynomials
Find the sum.
a. (2x3 – 5x2 + x) + (2x2 + x3 – 1)
b. (3x2 + x – 6) + (x2 + 4x + 10)
Warm-Up ExercisesEXAMPLE 3 Add polynomials
SOLUTION
a. Vertical format: Align like terms in vertical columns. (2x3 – 5x2 + x)
+ x3 + 2x2 – 1
3x3 – 3x2 + x – 1
b. Horizontal format: Group like terms and simplify.
(3x2 + x – 6) + (x2 + 4x + 10) =
= 4x2 + 5x + 4
(3x2 + x2) + (x + 4x) + (– 6 + 10)
Warm-Up ExercisesRewrite a polynomialEXAMPLE 1
Write 5y – 2y2 + 9 so that the exponents decrease from left to right. Identify the degree and leading coefficient of the polynomial.
1.
GUIDED PRACTICE for Examples 1,2, and 3
– 2y2 +5y + 9 Degree: 2, Leading Coefficient: –2
ANSWER
Tell whether y3 – 4y + 3 is a polynomial. If it is a polynomial, find its degree and classify it by the number of its terms. Otherwise, tell why it is not a polynomial.
2.
ANSWER
polynomial Degree: 3, trinomial
Warm-Up ExercisesEXAMPLE 3 Add polynomials
(5x3 + 4x – 2x) + (4x2 +3x3 – 6)
Find the sum.3.
GUIDED PRACTICE for Example for Examples 1,2, and 3
= 8x3 + 4x2 + 2x – 6ANSWER
Warm-Up ExercisesEXAMPLE 4 Subtract polynomials
Find the difference.
a. (4n2 + 5) – (–2n2 + 2n – 4)
b. (4x2 – 3x + 5) – (3x2 – x – 8)
Warm-Up ExercisesEXAMPLE 4 Subtract polynomials
SOLUTION
a. (4n2 + 5) 4n2 + 5
–(–2n2 + 2n – 4) 2n2 – 2n + 4
6n2 – 2n + 9
b. (4x2 – 3x + 5) – (3x2 – x – 8) =
= (4x2 – 3x2) + (–3x + x) + (5 + 8)
= x2 – 2x + 13
4x2 – 3x + 5 – 3x2 + x + 8
Warm-Up ExercisesEXAMPLE 5 Solve a multi-step problem
BASEBALL ATTENDANCE
Major League Baseball teams are divided into two leagues. During the period 1995–2001, the attendance N and A (in thousands) at National and American League baseball games, respectively, can be modeled by
N = –488t2 + 5430t + 24,700 and
where t is the number of years since 1995. About how many people attended Major League Baseball games in 2001?
A = –318t2 + 3040t + 25,600
Warm-Up ExercisesEXAMPLE 5 Solve a multi-step problem
SOLUTION
STEP 1
Add the models for the attendance in each league to find a model for M, the total attendance (in thousands).
M = (–488t2 + 5430t + 24,700) + (–318t2 + 3040t + 25,600)
= (–488t2 – 318t2) + (5430t + 3040t) + (24,700 + 25,600)
= –806t2 + 8470t + 50,300
Warm-Up ExercisesEXAMPLE 5 Solve a multi-step problem
STEP 2
Substitute 6 for t in the model, because 2001 is 6 years after 1995.
M = –806(6)2 + 8470(6) + 50,300 72,100
ANSWER
About 72,100,000 people attended Major League Baseball games in 2001.
Warm-Up ExercisesEXAMPLE 4 Subtract polynomials
a. (4x2 – 7x) – (5x2 + 4x – 9)
GUIDED PRACTICE for Examples 4 and 5
Find the difference.4.
–x2 – 11x + 9ANSWER
BASEBALL ATTENDNCE Look back at Example 5. Find the difference in attendance at National and American League baseball games in 2001.
5.
ANSWER about 7,320,000 people
Warm-Up ExercisesDaily Homework Quiz
If the expression is a polynomial, find its degree and classify it by the number of terms. Otherwise, tell why it is not a polynomial.
1. m3 + n4m2 + m–2
No; one exponent is not a whole number.
ANSWER
2. – 3b3c4 – 4b2c + c8
ANSWER 8th degree trinomial
Warm-Up ExercisesDaily Homework Quiz
Find the sum or difference.
3. (3m2 – 2m + 9) + (m2 + 2m – 4)
4m2 + 5ANSWER
4. (– 4a2 + 3a – 1) – (a2 + 2a – 6)
ANSWER –5a2 + a + 5
Warm-Up ExercisesDaily Homework Quiz
5. The number of dog adoptions D and cat adoptions C can be modeled by D = 1.35 t2 – 9.8t + 131 and C= 0.1t2 – 3t + 79 where t represents the years since 1998. About how many dogs and cats were adopted in 2004?
about 185 dogs and catsANSWER