Question

which expressions are factors of this polynomial?2x to the 4th power+ x to the 3rd power -29x to the 2nd power -34x + 24

Answer 1

The xpression is:

`2x^4+x^3-29x^2-34x+24`

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,

`\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}`

So, this is a factor.

2.

x - 3,

x- 3 = 0

x = 3

Plugging in x = 3

We have:

`\begin{gathered} 2x^4+x^3-29x^2-34x+24 \\ =2(3)^4+(3)^3-29(3)^2-34(3)+24 \\ =-150 \end{gathered}`

Not a factor.

3.

x - 4,

x - 4 = 0

x = 4

Substituting,

`\begin{gathered} 2(4)^4+(4)^3-29(4)^2-34(4)+24 \\ =0 \end{gathered}`

Is a factor.

4.

x + 6,

x + 6 = 0

x = -6

Substituting,

`\begin{gathered} 2(-6)^4+(-6)^3-29(-6)^2-34(-6)+24 \\ =1560 \end{gathered}`

Not a factor.

5.

x + 2,

x + 2 = 0

x = -2

Substituting,