Question

select all the possible values of be that make the trinomial factorable. List of values of be from least to greatest 2x^2 +bx+15

Answer 1

We are given the following polynomial

`2x^2+bx+15`

We are asked to find the possible values of b that make the trinomial factorable.

The value of b must be such that

`\begin{gathered} p\cdot q=30\quad (2*15=30) \\ b=p+q \end{gathered}`

So what could be the two numbers so that their product will be 30?

How about 30 and 1?

`\begin{gathered} 30\cdot1=30 \\ b=30+1=31_{} \end{gathered}`

So, b = 31 is one of the possible values.

How about 15 and 2?

`\begin{gathered} 15\cdot2=30 \\ b=15+2=17 \end{gathered}`

So, b = 17 is one of the possible values.

How about 10 and 3?

`\begin{gathered} 10\cdot3=30 \\ b=10+3=13 \end{gathered}`

So, b = 13 is one of the possible values.

How about 6 and 5?

`\begin{gathered} 6\cdot5=30 \\ b=6+5=11 \end{gathered}`

So, b = 11 is one of the possible values.

Therefore, all the possible values of b from least to greatest are

`b=11,13,17,31`