pre-algebra 13-1 polynomials pre-algebra homework page 654 #1-14
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Pre-Algebra
13-1 Polynomials
Pre-Algebra HOMEWORK
Page 654
#1-14
Our Learning Goal
Students will be able to classify, simplify,
add and subtract polynomials.
Pre-Algebra
13-1 Polynomials
Students will be able to classify, simplify, add and subtract polynomials by completing the
following assignments.
•Learn to classify polynomials by degree and by
the number of terms.
•Learn to simplify polynomials.
•Learn to add polynomials.
•Learn to subtract polynomials. …..and that’s all folks!
Pre-Algebra
13-1 Polynomials
Today’s Learning Goal Assignment
Learn to classify polynomials by degree and by the number of terms.
Pre-Algebra
13-1 Polynomials
13-1 Polynomials
Pre-Algebra
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Warm UpIdentify the base and exponent of each power.
1. 34 2. 2a 3. x5
Determine whether each number is a whole number.4. 0 5. –3 6. 5
3; 4 2; a x; 5
Pre-Algebra
13-1 Polynomials
yes no yes
Problem of the Day
If you take a whole number n, raise it to the third power, and then divide the result by n, what is the resulting expression? n2
Pre-Algebra
13-1 Polynomials
Learn to classify polynomials by degree and by the number of terms.
Pre-Algebra
13-1 Polynomials
Vocabulary
monomialpolynomialbinomialtrinomialdegree of a polynomial
Insert Lesson Title Here
Pre-Algebra
13-1 Polynomials
The simplest type of polynomial is called a monomial. A monomial is a number or a product of numbers and variables with exponents that are whole numbers.
Monomials 2n, x3, 4a4b3, 7
Not monomials p2.4, 2x, √x, g25
Pre-Algebra
13-1 Polynomials
monomial not a monomial
3 and 4 are whole numbers.
Additional Example 1: Identifying Monomials
Determine whether each expression is a monomial.
y does not have a exponent that is a whole number.
B. 3x3√y
Pre-Algebra
13-1 Polynomials
A. √2 • x3y4
Try This: Example 1
Determine whether each expression is a monomial.
A. 2w • p3y8 B. 9t3.2z
monomial not a monomial
3 and 8 are whole numbers.
3.2 is not a whole number.
Pre-Algebra
13-1 Polynomials
A polynomial is one monomial or the sum or difference of monomials. Polynomials can be classified by the number of terms. A monomial has 1 term, a binomial has 2 term, and a trinomial has 3 terms.
Pre-Algebra
13-1 Polynomials
Additional Example 2: Classifying Polynomials by the Number of Terms
Classify each expression as a monomial, a binomial, a trinomial, or not a polynomial.
A. xy2
B. 2x2 – 4y–2
C. 3x5 + 2.2x2 – 4
D. a2 + b2
monomial Polynomial with 1 term.
not a polynomial –2 is not a whole number.
trinomial Polynomial with 3 terms.
binomial Polynomial with 2 terms.
Pre-Algebra
13-1 Polynomials
Try This: Example 2
Classify each expression as a monomial, a binomial, a trinomial, or not a polynomial.
A. 4x2 + 7z4
B. 1.3x2.5 – 4y
C. 6.3x2
D. c99 + p3
binomial Polynomial with 2 terms.
not a polynomial 2.5 is not a whole number.
monomial Polynomial with 1 term.
binomial Polynomial with 2 terms.
Pre-Algebra
13-1 Polynomials
A polynomial can also be classified by its degree. The degree of a polynomial is the degree of the term with the greatest degree.
4x2 + 2x5 + x + 5
Degree 2 Degree 5 Degree 1 Degree 0
Degree 5
Pre-Algebra
13-1 Polynomials
Additional Example 3A & 3B: Classifying Polynomials by Their Degrees
Find the degree of each polynomial.
A. x + 4
B. 5x – 2x2 + 6
Degree 1 Degree 0 x + 4
The degree of x + 4 is 1.
Degree 1 Degree 2 Degree 0 5x – 2x2 + 6
The degree of 5x – 2x2 + 6 is 2.
Pre-Algebra
13-1 Polynomials
Try This: Example 3A & 3B
Find the degree of each polynomial.
A. y + 9.9
B. x + 4x4 + 2y
Degree 1 Degree 0 y + 9.9
The degree of y + 9.9 is 1.
Degree 1 Degree 4 Degree 1 x + 4x4 + 2y
The degree of x + 4x4 + 2y is 4.
Pre-Algebra
13-1 Polynomials
Additional Example 3C: Classifying Polynomials by Their Degrees
Find the degree of the polynomial.
C. –3x4 + 8x5 – 4x6
Degree 4 Degree 5 Degree 6
–3x4 + 8x5 – 4x6
The degree of –3x4 + 8x5 – 4x6 is 6.
Pre-Algebra
13-1 Polynomials
Try This: Example 3C
Find the degree of each polynomial.
C. –6x4 – 9x8 + x2
Degree 4 Degree 8 Degree 2
–6x4 – 9x8 + x2
The degree of –6x4 – 9x8 + x2 is 8.
Pre-Algebra
13-1 Polynomials
Additional Example 4: Physics Application
The height in feet after t seconds of a rocket launched straight up into the air from a 40-foot platform at velocity v is given by the polynomial –16t2 + vt + s. Find the height after 10 seconds of a rocket launched at a velocity of 275 ft/s.
Write the polynomial expression for height. –16t + vt + s
–1600 + 2750 + 40
–16(10)2 + 275(10) + 40 Substitute 10 for t, 275 for v, and 40 for s. Simplify.
1190
The rocket is 1190 ft high 10 seconds after launching.
Pre-Algebra
13-1 Polynomials
Try This: Example 4
The height in feet after t seconds of a rocket launched straight up into the air from a 20-foot platform at velocity v is given by the polynomial -16t2 + vt + s. Find the height after 15 seconds of a rocket launched at a velocity of 250 ft/s.
Write the polynomial expression for height. –16t2 + vt + s
–3600 + 3750 + 20
–16(15)2 + 250(15) + 20 Substitute 15 for t, 250 for v, and 20 for s. Simplify.
170
The rocket is 170 ft high 15 seconds after launching.
Pre-Algebra
13-1 Polynomials
Lesson Quiz
noyes
Insert Lesson Title Here
trinomial binomial
5 3
Determine whether each expression is a monomial.
1. 5a2z4 2. 3√x
Classify each expression as a monomial, a binomial, a trinomial, or not a polynomial.
3. 2x – 3x – 6 4. 3m3+ 4m
Find the degree of each polynomial.
5. 3a2 + a5 + 26 6. 2c3 – c2
Pre-Algebra
13-1 Polynomials