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3 years ago

The work shows how to use long division to find (x2 + 3x –9) ÷ (x – 2).

Mathematics

1 answer:

Maksim231197 [3]3 years ago

8 0

2x+3x -9. You can simplify this to 5x-9.

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What is the solution to | 2x-4| >8?

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$| 2x-4| \ \textgreater \ 8 \\ \\ 2x - 4 \ \textgreater \ 8 \ , \ -(2x - 4) \ \textgreater \ 8 \ / \ break \ problem \ into \ 2 \ equations \\ \\ first \ equation \\ \\ 2x \ \textgreater \ 8 + 4 \ / \ add \ 4 \ to \ each \ side \\ \\ 2x \ \textgreater \ 12 \ / \ simplify \\ \\ x \ \textgreater \ \frac{12}{2} \ / \ divide\ each \ side \ by \ 2 \\ \\ x \ \textgreater \ 6 \ / \ simplify \\ \\ second \ equation \\ \\ -2x + 4 \ \textgreater \ 8 \ / \ simplify \\ \\ -2x \ \textgreater \ 8 - 4 \ / \ subtract \ 4 \ from \ each \ side \\ \\ -2x \ \textgreater \ 4 \ / \ simplify \\ \\ x \ \textless \ \frac{4}{-2} \ / \ divide \ each \ side \ by \ -2 \\ \\$
$\\ \\ x \ \textless \ - \frac{4}{2} \ / \ simplify \\ \\ x \ \textless \ - 2 \ / \ simplify \\ \\ collect \ solutions \\ \\ x \ \textgreater \ 6 \ , \ x \ \textless \ -2 \\ \\$

So, your answer to this problem is x > 6 and x < -2.

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2 years ago

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Step-by-step explanation:

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2 years ago

Write the cubic polynomial function f(x)in expanded form with zeros −6,−5,and −1, given that f(0)=60

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Answer:

$f(x)=2x^{3}+24x^{2}+82x+60$

Step-by-step explanation:

we know that

The roots of the polynomial are the values of x when the value of the polynomial f(x) is equal to zero

The roots of the polynomial function are

x=-6 -----> (x+6)=0

x=-5 -----> (x+5)=0

x=-1 -----> (x+1)=0

The equation of the cubic polynomial is

$f(x)=a(x+6)(x+5)(x+1)$

where

a is the leading coefficient

Remember that

f(0)=60

That means ------> For x=0 the value of f(x) is equal to 60

substitute the value of x and the value of y in the function and solve for a

$60=a(0+6)(0+5)(0+1)$

$60=a(6)(5)(1)$

$60=30a$

$a=2$

$f(x)=2(x+6)(x+5)(x+1)$

Applying the distributive property

Convert to expanded form

$f(x)=2(x+6)(x+5)(x+1)\\\\f(x)=2(x+6)(x^{2}+x+5x+5)\\\\f(x)=2(x+6)(x^{2}+6x+5)\\\\f(x)=2(x^{3}+6x^{2}+5x+6x^{2}+36x+30)\\\\f(x)=2x^{3}+24x^{2}+82x+60$

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