MATHEMATICS HIGH SCHOOL

Select the correct answer.What is the factored form of 1,458x3 − 2?

A.
2(9x − 1)(81x2 + 9x + 1)
B.
2(9x + 1)(81x2 − 9x + 1)
C.
(9x − 2)(81x2 + 18x + 4)
D.
(9x + 2)(81x2 − 18x + 4)

Answers

Answer 1
Answer:

\huge \boxed{\mathbb{QUESTION} \downarrow}

What is the factored form of 1,458x³ − 2?

A. 2(9x − 1)(81x² + 9x + 1)

B. 2(9x + 1)(81x² − 9x + 1)

C. (9x − 2)(81x² + 18x + 4)

D. (9x + 2)(81x² − 18x + 4)

\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}

\sf \: 1458 x ^ { 3 } - 2

Factor out 2 (common factor).

\sf \: 2\left(729x^(3)-1\right)

Consider 729x^(3)-1. Rewrite 729x^(3)-1 as \left(9x\right)^(3)-1^(3). The difference of cubes can be factored using the rule: a^(3)-b^(3)=\left(a-b\right)\left(a^(2)+ab+b^(2)\right).

\sf\left(9x-1\right)\left(81x^(2)+9x+1\right)

Rewrite the complete factored expression. Polynomial 81x²+9x+1 is not factored as it does not have any rational roots.

\boxed{ \boxed{ \bf A) \: \: 2\left(9x-1\right)\left(81x^(2)+9x+1\right) }}

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I think you want the least common multipule (exg LCM of 2,3,4 is 12)

so we find the factors and include all of them so like this

15=3 times 5
12=2 times 2 times 3
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so to include all of them we include 3 2's, 1 3 and 1 5 or 2 times 2 times 2 times 3 times 5 or 8 times 15 or 4 times 30 or 120

the LCM is 120

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add 32/120+10/120+45/120=(32+10+45)/120=87/120
The least common denominator would be the least common multiple (LCM) of the denominators, 15 12 and 8.

To find the LCM, multiply two of the numbers together and test to see if the third one divides evenly into it.

15 x 8 = 120

120 ÷ 12 = 10

Because all three numbers go evenly into 120 (and 120 is the smallest number for which that is true), the least common denominator would be 120.

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