The xpression is:
[tex]2x^4+x^3-29x^2-34x+24[/tex]To find which of them is a factor, we equate factor to 0 and find the corresponding x value.
We put it in the polynomial expression.
If it gives 0 as the answer, it is a factor, otherwise, NOT.
So,
1.
2x - 1 = 0 ,
x = 1/2
Plugging in x = 1/2,
[tex]\begin{gathered} 2x^4+x^3-29x^2-34x+24 \\ =2(0.5)^4^{}+(0.5)^3-29(0.5)^2-34(0.5)+24 \\ =0 \end{gathered}[/tex]So, this is a factor.
2.
x - 3,
x- 3 = 0
x = 3
Plugging in x = 3
We have:
[tex]\begin{gathered} 2x^4+x^3-29x^2-34x+24 \\ =2(3)^4+(3)^3-29(3)^2-34(3)+24 \\ =-150 \end{gathered}[/tex]Not a factor.
3.
x - 4,
x - 4 = 0
x = 4
Substituting,
[tex]\begin{gathered} 2(4)^4+(4)^3-29(4)^2-34(4)+24 \\ =0 \end{gathered}[/tex]Is a factor.
4.
x + 6,
x + 6 = 0
x = -6
Substituting,
[tex]\begin{gathered} 2(-6)^4+(-6)^3-29(-6)^2-34(-6)+24 \\ =1560 \end{gathered}[/tex]Not a factor.
5.
x + 2,
x + 2 = 0
x = -2
Substituting,
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