ax"is the leading term, a is the leading coefficient, and a, is the constant term. The terms of a polynomial may be written in any order. However, if they are written in decreasing powers of, we say that the polynomial function is in standard form. Illustrative Example. A polynomial function f(x) = 4x° + 2x° + x + 6 can be written in standard form as f(x) = 2x'+ 4x + x+6. It is of degree 3; its leading term is 2x' ; its leading coefficient is 2; and its constant term is 6. Activity 1: Fix and Move Them, then Fill Me UP Consider the given polynomial functions and fill in the table below. Polynomial Function Polynomial function in standard position Leading Coefficient Constant Term Degree 1. f(x) = 3x²- 2x' + x- 3 |2.f(x) = 3 + 3x'- 2x + x² 3. f(x) = 6x²- 2x + x – 3 4. f(x) = 1 + x-5x

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 66E
icon
Related questions
Question
100%
What is the answer if this questions
ull Globe ?
12:55 AM
1 @ 59%
Week 1 LAS 1_..
МАТНЕMАТICS 10
Quarter 2
Name:
Date:
Year and Section:
Parent/Guardian's Signature:
Week 1 LAS1: Illustrates Polynomial Functions
A polynomial function is a function of the form
P(x) = a_x
+ . + a,x + a, a̟#0,
n is a nonnegative integer,
a,a, ..., a are all real numbers called coefficients,
where
a x" is the leading term,
a_is the leading coefficient, and
a is the constant term.
The terms of a polynomial may be written in any order. However, if they are written in decreasing powers of,
we say that the polynomial function is in standard form.
Illustrative Example.
A polynomial function f(x) = 4x + 2x + x+6 can be written in standard form as f(x) = 2x'+ 4x + x + 6. It is of
degree 3; its leading term is 2x' ; its leading coefficient is 2; and its constant term is 6.
Activity 1: Fix and Move Them, then Fill Me UP
Consider the given polynomial functions and fill in the table below.
Polynomial Function
Polynomial function
in standard position
Degree
Leading Coefficient
Constant Term
|1. f(x) = 3x- 2x' +x- 3
2.f(x) = 3 + 3x. 2x + x
3. f(x) = 6x- 2x + x - 3
4. f(x) = 1+ x-5x
Transcribed Image Text:ull Globe ? 12:55 AM 1 @ 59% Week 1 LAS 1_.. МАТНЕMАТICS 10 Quarter 2 Name: Date: Year and Section: Parent/Guardian's Signature: Week 1 LAS1: Illustrates Polynomial Functions A polynomial function is a function of the form P(x) = a_x + . + a,x + a, a̟#0, n is a nonnegative integer, a,a, ..., a are all real numbers called coefficients, where a x" is the leading term, a_is the leading coefficient, and a is the constant term. The terms of a polynomial may be written in any order. However, if they are written in decreasing powers of, we say that the polynomial function is in standard form. Illustrative Example. A polynomial function f(x) = 4x + 2x + x+6 can be written in standard form as f(x) = 2x'+ 4x + x + 6. It is of degree 3; its leading term is 2x' ; its leading coefficient is 2; and its constant term is 6. Activity 1: Fix and Move Them, then Fill Me UP Consider the given polynomial functions and fill in the table below. Polynomial Function Polynomial function in standard position Degree Leading Coefficient Constant Term |1. f(x) = 3x- 2x' +x- 3 2.f(x) = 3 + 3x. 2x + x 3. f(x) = 6x- 2x + x - 3 4. f(x) = 1+ x-5x
ll Globe ?
12:55 AM
1 © 60%
Week 1 LAS 2...
MATHEMATICS 10
Quarter 2
Name:
Date:
Year and Section:
Parent/Guardian's Signature:
Week 1 LAS 2: Illustrates Polynomial Functions
Polynomials may also be written in factored form and as a product of irreducible factors, that is, a factor
that can no longer be factored using coefficients that are real numbers.
Here are some examples.
a. y = x-5x - 24 in factored form is y = (x- 8) (x + 3)
b. y = -x + 9x in factored form is y = x(x + 3)(x - 3)
c. y = 2x + 5x + 7x- 5 in factored form is y =( x + 3x + 5)(2x - 1)
d. f(x) = x + x + 18 in factored form is f(x) = (x²- 2x + 6)(x + 3)
e. f(x) = x +x - 12x in factored form is f(x) = x(x + 4)(x - 3)
Activity 2: Do You Miss Me? Here I am Again
Write the following polynomial functions in factored form.
1. f(x) = 2x -11x + 5
2. f(x) = x - 5x
3. f(x) = (2x - 5x + 3) (x - 3)
4. f(x) = x+ 5x + 6
5. f(x) = (x - 1) (x² - 5x + 6)
Transcribed Image Text:ll Globe ? 12:55 AM 1 © 60% Week 1 LAS 2... MATHEMATICS 10 Quarter 2 Name: Date: Year and Section: Parent/Guardian's Signature: Week 1 LAS 2: Illustrates Polynomial Functions Polynomials may also be written in factored form and as a product of irreducible factors, that is, a factor that can no longer be factored using coefficients that are real numbers. Here are some examples. a. y = x-5x - 24 in factored form is y = (x- 8) (x + 3) b. y = -x + 9x in factored form is y = x(x + 3)(x - 3) c. y = 2x + 5x + 7x- 5 in factored form is y =( x + 3x + 5)(2x - 1) d. f(x) = x + x + 18 in factored form is f(x) = (x²- 2x + 6)(x + 3) e. f(x) = x +x - 12x in factored form is f(x) = x(x + 4)(x - 3) Activity 2: Do You Miss Me? Here I am Again Write the following polynomial functions in factored form. 1. f(x) = 2x -11x + 5 2. f(x) = x - 5x 3. f(x) = (2x - 5x + 3) (x - 3) 4. f(x) = x+ 5x + 6 5. f(x) = (x - 1) (x² - 5x + 6)
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage