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:

Machine-Hours

A measure of production time based on the number of hours machines are operating.

Unused Capacity

Available production or service facilities that are currently not in use or are underutilized.

Predetermined Overhead Rate

A projected rate applied for distributing manufacturing overhead expenses across specific products or job orders.

Machine-Hours

A measure of the total time that manufacturing equipment is operating during a specific period, often used as a basis for allocating manufacturing overhead.