Answered

Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Get accurate and detailed answers to your questions from a dedicated community of experts on our Q&A platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

Learning Task 1: Write and answer the following in your answer sheet
1. Evaluate the following polynomials in your answer sheet.
f(x) = x4 – 7x2 + 2x - 6
x=1
b. f(x) = 10x3 + 4x2 - 5
x = -3
f(x) = x4 + 5x3 - 2x + 3
a.
at
at
C.
find (2))2
2. Factor each polynomial completely using any method
(x + 1)(x2 – 5x + 6)
b. (x2 - * - 6)(x2 + 6x + 9)
x3 + 3x2 - 4x - 12
a.
C.
LABAR

Learning Task 1 Write And Answer The Following In Your Answer Sheet 1 Evaluate The Following Polynomials In Your Answer Sheet Fx X4 7x2 2x 6 X1 B Fx 10x3 4x2 5 class=

Sagot :

Answer:

Evaluating Polynomials:

a. f(1) = -10  

b. f(-3) = -239  

c. f(2)² = 3125

Factoring Polynomials:

a. (x + 1)(x² - 5x + 6) = (x + 1)(x - 3)(x - 2)  

b. (x² - x - 6)(x² + 6x + 9) = (x - 3)(x + 2)(x + 3)(x + 3)  

c. x³ + 3x² - 4x - 12 = (x + 3)(x - 2)(x + 2)(x - 2)(x + 2)  

MrRoyal

A polynomial can be evaluated and factored by long division, factoring and synthetic division methods.

1. Evaluate polynomials

[tex]\mathbf{f(x) = x^4 - 7x^2 + 2x - 6}[/tex]

Substitute 1 for x

[tex]\mathbf{f(1) = 1^4 - 7(1)^2 + 2(1) - 6}[/tex]

[tex]\mathbf{f(1) = 1 - 7 + 2 - 6}[/tex]

[tex]\mathbf{f(1) = -10}[/tex]

[tex]\mathbf{f(x) = 10x^3 + 4x^2 - 5}[/tex]

Substitute -3 for x

[tex]\mathbf{f(-3) = 10(-3)^3 + 4(-3)^2 - 5}[/tex]

[tex]\mathbf{f(-3) = -270 + 36 - 5}[/tex]

[tex]\mathbf{f(-3) = -239}[/tex]

[tex]\mathbf{f(x) =x^4 + 5x^3 - 2x + 3}[/tex]

Substitute 2 for x

[tex]\mathbf{f(2) =2^4 + 5(2)^3 - 2(2) + 3}[/tex]

[tex]\mathbf{f(2) =16 + 40 - 4 + 3}[/tex]

[tex]\mathbf{f(2) =55}[/tex]

Square both sides

[tex]\mathbf{f(2)^2 =3025}[/tex]

Hence, the results of evaluating the polynomials are [tex]\mathbf{f(1) = -10}[/tex], [tex]\mathbf{f(-3) = -239}[/tex] and [tex]\mathbf{f(2)^2 =3025}[/tex]

2. Factor the polynomials

[tex]\mathbf{(x + 1)(x^2 - 5x + 6)}[/tex]

Expand

[tex]\mathbf{(x + 1)(x^2 - 5x + 6) =(x + 1)(x^2 - 2x - 3x + 6) }[/tex]

Factorize

[tex]\mathbf{(x + 1)(x^2 - 5x + 6) =(x + 1)(x(x - 2) - 3(x - 2) )}[/tex]

Factor out x - 2

[tex]\mathbf{(x + 1)(x^2 - 5x + 6) =(x + 1)(x - 3)(x - 2) }[/tex]

[tex]\mathbf{(x^2 - x - 6)(x^2 + 6x + 9)}[/tex]

Expand

[tex]\mathbf{(x^2 - x - 6)(x^2 + 6x + 9) = (x^2 +2x - 3x - 6)(x^2 + 3x +3x + 9)}[/tex]

Factorize

[tex]\mathbf{(x^2 - x - 6)(x^2 + 6x + 9) = [x(x +2) - 3(x + 2)][x(x + 3) +3(x + 3)]}[/tex]

Factor out x + 2 and x + 3

[tex]\mathbf{(x^2 - x - 6)(x^2 + 6x + 9) = [(x - 3) (x + 2)][(x + 3)(x + 3)]}[/tex]

Remove square brackets

[tex]\mathbf{(x^2 - x - 6)(x^2 + 6x + 9) = (x - 3) (x + 2)(x + 3)(x + 3)}[/tex]

[tex]\mathbf{x^3 + 3x^2 - 4x - 12}[/tex]

Factorize

[tex]\mathbf{x^3 + 3x^2 - 4x - 12 = x^2(x + 3) - 4(x + 3)}[/tex]

Factor out x + 3

[tex]\mathbf{x^3 + 3x^2 - 4x - 12 = (x^2 -4) (x + 3)}[/tex]

Apply the difference of two squares

[tex]\mathbf{x^3 + 3x^2 - 4x - 12 = (x -2)(x+2) (x + 3)}[/tex]

Hence, the results of factoring the polynomials are [tex]\mathbf{(x + 1)(x^2 - 5x + 6) =(x + 1)(x - 3)(x - 2) }[/tex], [tex]\mathbf{(x^2 - x - 6)(x^2 + 6x + 9) = (x - 3) (x + 2)(x + 3)(x + 3)}[/tex] and [tex]\mathbf{x^3 + 3x^2 - 4x - 12 = (x -2)(x+2) (x + 3)}[/tex]

Read more about polynomials at:

https://brainly.com/question/11536910

Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.