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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

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