Step-by-step explanation:Look at this as 2 separate expressions for now, being the first 2 terms and...

Mathematics, 17.01.2022 16:00 garzar7523

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Answer from: morgan15776

(x+1)(x-1)(x-2)

Step-by-step explanation:

x^3-2x^2-x+2

Look at this as 2 separate expressions for now, being the first 2 terms and the last 2 terms:

$\mbox{1. }x^3-2x^2\\\mbox{2. }-x+2$

Factor both of these individually, starting with the first one. The greatest common factor here is x², so factor that out:

$\rightarrow x^3-2x^2\\\rightarrow x^2(x-2)$

Now the second equation. There isn't really a GCF here, but you still should factor out a -1 to get the x on its own.

$\rightarrow -x+2\\\rightarrow -1(x-2)$

Together, that leaves you with this:

x^2(x-2)-1(x-2)

This is actually another expression that can be factored. The GCF here is (x - 2):

$\rightarrow x^2(x-2)-1(x-2)\\\rightarrow (x^2-1)(x-2)$

Finally, you can expand that (x² - 1) further using this rule:

(x^2-y^2)=(x+y)(x-y)

1 is equal to 1², so you can rewrite that term and then expand it with the rule above:

$\rightarrow (x^2-1^2)(x-2)\\\rightarrow (x+1)(x-1)(x-2)$

Answer from: cbaublitz

${x}^{3} - {2x}^{2} - x + 2 \\ = {x}^{2} (x - 2) - 1(x - 2) \\ = ( {x}^{2} - 1)(x - 2) \\ = ( {(x)}^{2} - {(1)}^{2} )(x - 2) \\ = (x + 1)(x - 1)(x - 2)$

Answer:

(x + 1)(x - 1)(x - 2)

Hope you could understand.

If you have any query, feel free to ask.

Answer from: Quest

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

Answer from: Quest

step-by-step explanation:

the ratio of red paint to blue paint is always 9/7. that means that, whatever x's value, (4x+12)/(4x-4) has that same ratio. so, set up an equation and cross-multiply to solve for x:

9/7 = (4x+12)/(4x-4)

9(4x-4) = 7(4x+12)

36x - 36 = 28x + 84

8x - 36 = 84

8x = 120

x = 15

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