Consider the Following Approach to Factoring $$20 x ^ { 2 } + 39 x + 18$$

question 130

Short Answer

Consider the following approach to factoring. $$20 x ^ { 2 } + 39 x + 18$$ We need two integers whose sum is 39 and whose product is 360. To help find these integers, let s prime factor 360. $360 = 5 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5$ Now by grouping these factors in various ways, we find that $2 \cdot 2 \cdot 2 \cdot 3 = 24,3 \cdot 5 = 15$ and $24 + 15 = 39$ So the numbers are 15 and 24, and we can express the middle term of the given trinomial, $39 x$ , as $15 x + 24 x$ . Therefore, we can complete the factoring as follows: $20 x ^ { 2 } + 39 x + 18 = 20 x ^ { 2 } + 15 x + 24 x + 18 = 5 x ( 4 x + 3 ) + 6 ( 4 x + 3 ) = ( 4 x + 3 ) ( 5 x + 6 )$ Factor the trinomial. $20 y ^ { 2 } + 9 y + 1$

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Definitions:

Residual Income

The income that remains after deducting all required costs of capital from the operating income.

Imputed Interest

The interest that is considered or assumed to be charged on an interest-free loan or bond, often for tax calculations.

Residual Income

The income that remains after subtracting all the costs of capital from the net operating income.

Net Operating Income

Earnings before interest and taxes (EBIT), a measure of a company's profitability from operations.