Question

Please give the key idea of the lesson as given by the instructor. You must watch the recording to complete correctly. (What is the factored form of)

Answer 1

I'm not sure how to answer problem 1. I'll answer problem 2 only.

Answer: Choice A.
`(3\text{x}^2+5)(6\text{x}-1)`

Work Shown

`18\text{x}^3-3\text{x}^2+30\text{x}-5\\\\(18\text{x}^3-3\text{x}^2)+(30\text{x}-5)\\\\3\text{x}^2(6\text{x}-1)+5(6\text{x}-1)\\\\(3\text{x}^2+5)(6\text{x}-1)`

For more information and other examples, search out "factor by grouping".

Use the FOIL rule or the distributive property to expand out the answer, and you should get the original expression again. This is one way to confirm the answer is correct.

Answer 2

The expression 18³ - 3x² + 30x - 5 can be factored as (3x² - 5)(6x - 1).

Explanation:

The factored form of the expression 18³ - 3x² + 30x - 5 is (3x² - 5)(6x - 1).

To find the factored form, we need to factor out the expression.

Step 1: Look for common factors among the terms. In this case, there are no common factors.

Step 2: Check if the expression is a perfect square trinomial. In this case, it is not.

Step 3: Use the grouping method or trial and error to factor the expression.

The expression 18³ - 3x² + 30x - 5 can be factored as (3x² - 5)(6x - 1).