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3 years ago

Write the difference in factored form. (24x4 - 15x2 + 6x) - (10x4 + 5x2 - 4x)

Mathematics

1 answer:

Pachacha [2.7K]3 years ago

8 0

Answer:

The factored difference is: $2x(7x^3 - 10x + 5)$

Step-by-step explanation:

Difference in non factored form:

To find the difference in non-factored form, we subtract the common terms. So

$24x^4 - 15x^2 + 6x - (10x^4 + 5x^2 - 4x) = 24x^4 - 10x^4 - 15x^2 - 5x^2 + 6x + 4x = 14x^4 - 20x^2 + 10x$

Greatest common factor:

Of the exponents: Between $x^4, x^2$ and $x$ , it is the one with the lowest exponent, so x.

Between 14, 20 and 10:

14 - 20 - 10|2

7 - 10 - 5

So 2

The gcf is 2x, which means that the factored expression is:

$2x(\frac{14x^4}{2x} - \frac{20x^2}{2x} + \frac{10x}{2x}) = 2x(7x^3 - 10x + 5)$

The factored difference is: $2x(7x^3 - 10x + 5)$

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Solve for x.<br> 6(x - 1) = 9(x + 2)<br> x = -8<br> X = -3<br> X = 3<br> x = 8

Wewaii [24]

Answer:

$x=-8$

Step-by-step explanation:

$6\left(x-1\right)=9\left(x+2\right)\\\mathrm{Expand\:}6\left(x-1\right):\quad 6x-6\\6\left(x-1\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b-c\right)=ab-ac\\a=6,\:b=x,\:c=1\\=6x-6\cdot \:1\\\mathrm{Expand\:}9\left(x+2\right):\quad 9x+18\\9\left(x+2\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\a=9,\:b=x,\:c=2\\=9x+9\cdot \:2\\\mathrm{Multiply\:the\:numbers:}\:9\cdot \:2=18\\=9x+18\\6x-6=9x+18\\\mathrm{Add\:}6\mathrm{\:to\:both\:sides}$

$6x-6+6=9x+18+6\\Simplify\\6x=9x+24\\\mathrm{Subtract\:}9x\mathrm{\:from\:both\:sides}\\6x-9x=9x+24-9x\\Simplify\\-3x=24\\\mathrm{Divide\:both\:sides\:by\:}-3\\\frac{-3x}{-3}=\frac{24}{-3}\\Simplify\\\frac{-3x}{-3}=\frac{24}{-3}\\\mathrm{Simplify\:}\frac{-3x}{-3}:\quad x\\\frac{-3x}{-3}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{-b}=\frac{a}{b}\\=\frac{3x}{3}\\\mathrm{Divide\:the\:numbers:}\:\frac{3}{3}=1\\=x\\\mathrm{Simplify\:}\frac{24}{-3}:\quad -8\\\frac{24}{-3}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{-b}=-\frac{a}{b}\\=-\frac{24}{3}\\\mathrm{Divide\:the\:numbers:}\:\frac{24}{3}=8\\=-8\\$

4 0

3 years ago

Read 2 more answers

If the point (3,5) is on f(x) find the corresponding point on the graph of y=(x+2)+1

ad-work [718]

The corresponding point to the point given (3,5) which is on the graph of f(x) as described in the task content is; (3,6).

<h3>What is the corresponding point to the given point (3,5) as given in the task?</h3>

It follows from the task content that the point given originally is; (3,5).

However, it is required that the point which is equivalent to the given point on the graph of y=(x+2)+1 be identified.

It therefore follows that the point required as in discuss is;

y = (3+2) +1

y = 6.

Hence, the corresponding point is; (3,6).

Write the difference in factored form. (24x4 - 15x2 + 6x) - (10x4 + 5x2 - 4x)​

Write the difference in factored form. (24x4 - 15x2 + 6x) - (10x4 + 5x2 - 4x)