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3 years ago

How does finding the greatest common factor help you solve real-world problems

Mathematics

1 answer:

olchik [2.2K]3 years ago

3 0

It allows you to do simple multiplicative and division problems faster

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If f(x)=x^3-12x^2+35x-24f(x)=x 3 −12x 2 +35x−24 and f(8)=0f(8)=0, then find all of the zeros of f(x)f(x) algebraically.

Neporo4naja [7]

Answer:

The zeros of f(x) are: (x - 1), (x - 3) and (x - 8)

Step-by-step explanation:

Given

$f(x)=x^3-12x^2+35x-24$

$f(8) = 0$

Required

Find all zeros of the f(x)

If $f(8) = 0$ then:

$x = 8$

And $x - 8$ is a factor

Divide f(x) by x - 8

$\frac{f(x)}{x - 8} = \frac{x^3-12x^2+35x-24}{x - 8}$

Expand the numerator

$\frac{f(x)}{x - 8} = \frac{x^3 - 4x^2 -8x^2 + 3x + 32x - 24}{x - 8}$

Rewrite as:

$\frac{f(x)}{x - 8} = \frac{x^3 - 4x^2 + 3x - 8x^2 +32x - 24}{x - 8}$

Factorize

$\frac{f(x)}{x - 8} = \frac{(x^2 - 4x + 3)(x - 8)}{x - 8}$

Expand

$\frac{f(x)}{x - 8} = \frac{(x^2 -x - 3x + 3)(x - 8)}{x - 8}$

Factorize

$\frac{f(x)}{x - 8} = \frac{(x - 1)(x - 3)(x - 8)}{x - 8}$

$\frac{f(x)}{x - 8} = (x - 1)(x - 3)$

Multiply both sides by x - 8

$f(x) = (x - 1)(x - 3)(x - 8)$

Hence, the zeros of f(x) are: (x - 1), (x - 3) and (x - 8)

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2 years ago

1. Write an expression for 8 less than 2 times a number.

Nuetrik [128]

Answer:

8<2x

Step-by-step explanation:

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2 years ago

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What is the slope of the line that goes through (2,7) (3,9)

marin [14]

Answer:

Step-by-step explanation:

slope (m) = y2 - y1/x2 - x1

m = 9 - 7/3 - 2

m = 2/1

m = 2

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3 years ago

Double a number decreased by 25.6 is equal to 90 Find the number

marin [14]

Answer:

Step-by-step explanation:

2x-25,6=90

2x=90+25,6

2x=115,6

x=57,8

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3 years ago

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What gives humans a particular advantage over other species in the use of commons?

Artemon [7]

Answer:

Humans have technology

Step-by-step explanation:

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