Respuesta :
We are given the following polynomial
[tex]2x^2+bx+15[/tex]We are asked to find the possible values of b that make the trinomial factorable.
The value of b must be such that
[tex]\begin{gathered} p\cdot q=30\quad (2\times15=30) \\ b=p+q \end{gathered}[/tex]So what could be the two numbers so that their product will be 30?
How about 30 and 1?
[tex]\begin{gathered} 30\cdot1=30 \\ b=30+1=31_{} \end{gathered}[/tex]So, b = 31 is one of the possible values.
How about 15 and 2?
[tex]\begin{gathered} 15\cdot2=30 \\ b=15+2=17 \end{gathered}[/tex]So, b = 17 is one of the possible values.
How about 10 and 3?
[tex]\begin{gathered} 10\cdot3=30 \\ b=10+3=13 \end{gathered}[/tex]So, b = 13 is one of the possible values.
How about 6 and 5?
[tex]\begin{gathered} 6\cdot5=30 \\ b=6+5=11 \end{gathered}[/tex]So, b = 11 is one of the possible values.
Therefore, all the possible values of b from least to greatest are
[tex]b=11,13,17,31[/tex]